Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
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Textbook Question
Chapter 3.1, Problem 43E
True or False
(a) The determinant of a
(b) The determinant of a matrix of order
(c) The
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Elementary Linear Algebra (MindTap Course List)
Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Find the determinant of the matrix in Exercise 15...Ch. 3.1 - Find the determinant of the matrix in Exercise 16...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Prob. 24ECh. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Prob. 32ECh. 3.1 - Finding a Determinant in Exercises 33 and 34, use...Ch. 3.1 - Finding a Determinant in Exercises 33 and 34, use...Ch. 3.1 - Finding a Determinant In Exercises 35-38, use a...Ch. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - True or False ? a The determinant of a 22 matrix A...Ch. 3.1 - True or False ? a To find the determinant of a...Ch. 3.1 - Solving an Equation In Exercises 45-48, solve for...Ch. 3.1 - Prob. 46ECh. 3.1 - Solving an Equation In Exercises 45-48, solve for...Ch. 3.1 - Solving an Equation In Exercises 45-48, solve for...Ch. 3.1 - Solving an Equation In Exercises 4952, find the...Ch. 3.1 - Solving an Equation In Exercises 4952, find the...Ch. 3.1 - Solving an Equation In Exercises 49-52, find the...Ch. 3.1 - Solving an Equation In Exercises 49-52, find the...Ch. 3.1 - Show that the system of linear equations...Ch. 3.1 - Prob. 54ECh. 3.1 - Entries Involving Expressions In Exercises 55- 62,...Ch. 3.1 - Prob. 56ECh. 3.1 - Entries Involving Expressions In Exercises 55-62,...Ch. 3.1 - Prob. 58ECh. 3.1 - Entries Involving Expressions In Exercises 55- 62,...Ch. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Verifying an Equation In Exercises 63-68, evaluate...Ch. 3.1 - Prob. 64ECh. 3.1 - Verify an Equation In Exercises 63-68, evaluate...Ch. 3.1 - Prob. 66ECh. 3.1 - Verifying an equation In Exercises 63-68, evaluate...Ch. 3.1 - Prob. 68ECh. 3.1 - You are given the equation |x0c1xb01a|=ax2+bx+c....Ch. 3.1 - The determinant of a 22 matrix involves two...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 6ECh. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 8ECh. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 10ECh. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 12ECh. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 16ECh. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 18ECh. 3.2 - Properties of Determinant In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Finding a Determinant In Exercises 2124, use...Ch. 3.2 - Finding a Determinant In Exercises 2124, use...Ch. 3.2 - Finding a Determinant In Exercises 2124, use...Ch. 3.2 - Prob. 24ECh. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 26ECh. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 28ECh. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 34ECh. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Proof Prove the property....Ch. 3.2 - Proof Prove the property....Ch. 3.2 - Find each determinant. a |cossinsincos| b...Ch. 3.2 - CAPSTONE Evaluate each determinant when a = 1, b =...Ch. 3.2 - Guided Proof Prove Property 2 of Theorem 3.3: When...Ch. 3.2 - Prob. 48ECh. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - Prob. 6ECh. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - Prob. 8ECh. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - Prob. 10ECh. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - Prob. 14ECh. 3.3 - The Determinant of a Matrix Sum In Exercises...Ch. 3.3 - Prob. 16ECh. 3.3 - The Determinant of a Matrix Sum In Exercises...Ch. 3.3 - Prob. 18ECh. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Prob. 20ECh. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Prob. 24ECh. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - Prob. 30ECh. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Prob. 42ECh. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 44ECh. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 46ECh. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 48ECh. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 50ECh. 3.3 - Finding Determinants In Exercises 51-56, use a...Ch. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Let A and B be square matrices of order 4 such...Ch. 3.3 - CAPSTONE Let A and B be square matrices of order 3...Ch. 3.3 - Proof Let A and B be nn matrices such that...Ch. 3.3 - Prob. 60ECh. 3.3 - Find two 22 matrices such that |A|+|B|=|A+B|.Ch. 3.3 - Prob. 62ECh. 3.3 - Let A be an nn matrix in which the entries of each...Ch. 3.3 - Illustrate the result of Exercise 63 with the...Ch. 3.3 - Guided Proof Prove that the determinant of an...Ch. 3.3 - Prob. 66ECh. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Orthogonal Matrices in Exercises 73-78, determine...Ch. 3.3 - Prob. 77ECh. 3.3 - Prob. 78ECh. 3.3 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.3 - Prob. 81ECh. 3.3 - Prob. 82ECh. 3.3 - Proof If A is an idempotent matrix (A2=A), then...Ch. 3.3 - Prob. 84ECh. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Prob. 2ECh. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 10ECh. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 20ECh. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Use Cramers Rule to solve the system of linear...Ch. 3.4 - Verify the system of linear equations in cosA,...Ch. 3.4 - Finding the Area of a Triangle In Exercises 29-32,...Ch. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Finding an Equation of a Line In Exercises 37-40,...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Testing for Coplanar Points In Exercises 47-52,...Ch. 3.4 - Testing for Coplanar Points In Exercises 47-52,...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Using Cramers Rule In Exercises 59 and 60,...Ch. 3.4 - Using Cramers Rule In Exercises 59 and 60,...Ch. 3.4 - Software Publishing The table shows the estimate...Ch. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - Prob. 70ECh. 3.CR - The Determinant of a Matrix In Exercises 1-18,...Ch. 3.CR - Prob. 2CRCh. 3.CR - Prob. 3CRCh. 3.CR - Prob. 4CRCh. 3.CR - Prob. 5CRCh. 3.CR - Prob. 6CRCh. 3.CR - Prob. 7CRCh. 3.CR - Prob. 8CRCh. 3.CR - Prob. 9CRCh. 3.CR - The Determinant of a Matrix In Exercises 1-18,...Ch. 3.CR - Prob. 11CRCh. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Prob. 14CRCh. 3.CR - Prob. 15CRCh. 3.CR - Prob. 16CRCh. 3.CR - Prob. 17CRCh. 3.CR - Prob. 18CRCh. 3.CR - Properties of Determinants In Exercises 19-22,...Ch. 3.CR - Properties of Determinants In Exercises 19-22,...Ch. 3.CR - Prob. 21CRCh. 3.CR - Prob. 22CRCh. 3.CR - Prob. 23CRCh. 3.CR - Prob. 24CRCh. 3.CR - Prob. 25CRCh. 3.CR - Prob. 26CRCh. 3.CR - Prob. 27CRCh. 3.CR - Finding Determinants In Exercises 27 and 28, find...Ch. 3.CR - Prob. 29CRCh. 3.CR - Prob. 30CRCh. 3.CR - Prob. 31CRCh. 3.CR - The Determinant of the Inverse of a Matrix In...Ch. 3.CR - Prob. 33CRCh. 3.CR - Prob. 34CRCh. 3.CR - Solving a System of Linear Equations In Exercises...Ch. 3.CR - Solving a System of Linear Equations In Exercises...Ch. 3.CR - Prob. 37CRCh. 3.CR - Prob. 38CRCh. 3.CR - System of Linear Equation In Exercises 37-42, use...Ch. 3.CR - System of Linear Equation In Exercises 37-42, use...Ch. 3.CR - Prob. 41CRCh. 3.CR - Prob. 42CRCh. 3.CR - Let A and B be square matrices of order 4 such...Ch. 3.CR - Prob. 44CRCh. 3.CR - Prob. 45CRCh. 3.CR - Prob. 46CRCh. 3.CR - Prob. 47CRCh. 3.CR - Show that |a1111a1111a1111a|=(a+3)(a1)3Ch. 3.CR - Prob. 49CRCh. 3.CR - Prob. 50CRCh. 3.CR - Prob. 51CRCh. 3.CR - Prob. 52CRCh. 3.CR - Prob. 53CRCh. 3.CR - Prob. 54CRCh. 3.CR - Prob. 55CRCh. 3.CR - Prob. 56CRCh. 3.CR - Prob. 57CRCh. 3.CR - Prob. 58CRCh. 3.CR - Prob. 59CRCh. 3.CR - Prob. 60CRCh. 3.CR - Prob. 61CRCh. 3.CR - Prob. 62CRCh. 3.CR - Prob. 63CRCh. 3.CR - Prob. 64CRCh. 3.CR - Prob. 65CRCh. 3.CR - Using Cramers Rule In Exercises 65 and 66, use a...Ch. 3.CR - Prob. 67CRCh. 3.CR - Prob. 68CRCh. 3.CR - Prob. 69CRCh. 3.CR - Prob. 70CRCh. 3.CR - Prob. 71CRCh. 3.CR - Prob. 72CRCh. 3.CR - Prob. 73CRCh. 3.CR - Health Care Expenditures The table shows annual...Ch. 3.CR - Prob. 75CRCh. 3.CR - Prob. 76CRCh. 3.CR - True or False? In Exercises 75-78, determine...Ch. 3.CR - Prob. 78CRCh. 3.CM - Prob. 1CMCh. 3.CM - Prob. 2CMCh. 3.CM - In Exercises 3and4, use Gaussian elimination to...Ch. 3.CM - In Exercises 3and4, use Gaussian elimination to...Ch. 3.CM - Use a software program or a graphing utility to...Ch. 3.CM - Prob. 6CMCh. 3.CM - Solve the homogeneous linear system corresponding...Ch. 3.CM - Determine the values of k such that the system is...Ch. 3.CM - Solve for x and y in the matrix equation 2AB=I,...Ch. 3.CM - Find ATA for the matrix A=[531246]. Show that this...Ch. 3.CM - In Exercises 11-14, find the inverse of the matrix...Ch. 3.CM - In Exercises 11-14, find the inverse of the matrix...Ch. 3.CM - Prob. 13CMCh. 3.CM - In Exercises 11-14, find the inverse of the matrix...Ch. 3.CM - In Exercises 15 and 16, use an inverse matrix to...Ch. 3.CM - In Exercises 15 and 16, use an inverse matrix to...Ch. 3.CM - Find the sequence of the elementary matrices whose...Ch. 3.CM - Find the determinant of the matrix....Ch. 3.CM - Find a |A|, b |B|, c AB and d |AB| then verify...Ch. 3.CM - Find a |A| and b |A1| A=[523104682]Ch. 3.CM - If |A|=7 and A is of order 4. Then find each...Ch. 3.CM - Use the adjoint of A=[151021102] to find A1Ch. 3.CM - Let X1,X2,X3 and b be the column matrices below....Ch. 3.CM - Use a system of linear equation to find the...Ch. 3.CM - Use a determinant to find an equation of the line...Ch. 3.CM - Use a determinant to find the area of the triangle...Ch. 3.CM - Determine the currents I1I2 and I3 for the...Ch. 3.CM - A manufacture produce three models of a product...Ch. 3.CM - Prob. 29CM
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- True or False ? a To find the determinant of a triangular matrix, add the entries on the main diagonal. b To find the determinant of a matrix, expand by cofactors in any row or column. c When expanding by cofactors, you need not evaluate the cofactors of zero entries.arrow_forwardGuided Proof Prove Property 2 of Theorem 3.3: When B is obtained from A by adding a multiple of a row of A to another row of A, detB = detA. Getting Started: To prove that the determinant of B is equal to the determinant of A, you need to show that their respective cofactor expansions are equal. i Begin by letting B be the matrix obtained by adding c times the jth row of A to the ith row of A. ii Find the determinant of B by expanding in this ith row. iii Distribute and then group the terms containing a coefficient of c and those not containing a coefficient of c. iv Show that the sum of the terms not containing a coefficient of c is the determinant of A, and the sum of the terms containing a coefficient of c is equal to 0.arrow_forwardTEST Only one of the following matrix has an inverse. Find the determinant of each matrix, and use the determinant to identify the one that has an inverse. Then find the inverse. A=[141020101] B=[140020301]arrow_forward
- Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is O. For simplicity, use a 22 .arrow_forwardFind the determinant of the matrix. [4032013501511103]arrow_forwardFind the determinant of the matrix in Exercise 16 using the method of expansion by cofactors. Use a the third row and b the first column. 16. [342631478]arrow_forward
- Find the determinant of the matrix in Exercise 15 using the method of expansion by cofactors. Use a the second row and b the second column. 15. [321456231]arrow_forwardThe determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six triple products. Show that the determinant of a 44 matrix involves 24 quadruple products.arrow_forwardGuided Proof Prove that the determinant of an invertible matrix A is equal to 1 when all of the entries of A and A1 is integers. Getting Started: Denote det(A) as x and det(A1) as y. Note that x and y are real numbers. To prove that det(A) is equal to 1, you must show that both x and y are integers such that their product xy is equal to 1. (i) Use the property for the determinant of a matrix product to show that xy=1. (ii) Use the definition of a determinant and the fact that the entries of A and A1 are integers to show that both x=det(A) and y=det(A1) are integers. (iii) Conclude that x=det(A) must be either 1 or 1 because these are the only integer solutions to the equation xy=1arrow_forward
- Find the determinant of the 33 matrix. det(A)=|137111123|arrow_forwardCollinear Points and Determinants a If three points lie on a line, what is the area of the triangle that they determine? Use the answer to this question, together with the determinant formula for the area of a triangle, to explain why the points (a1,b1), (a2,b2) and (a3,b3) are collinear if and only if |a1b11a2b21a3b31|=0 b Use a determinant to check whether each set of points is collinear. Graph them to verify your answer. i (6,4), (2,10), (6,13) ii (5,10), (2,6), (15,2)arrow_forward
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