1 Let v, = 4 V2 V3= -4 6. 1 -2 Using determinants in all of the following questions, verify that (a) The matrix P = [v, v, V3]is an invertible matrix. (b) Find the inverse of the matrix P. 1 (c) Solve the system X,Vq+X2V2+X3V3

Q: If the determinant of a 4 x 4 matrix A is det (A) = 4, and the matrix D is obtained from A by adding…

A: As we know that applying row(column) operation value of determinants will not changed.

Q: 1. Consider the following matrix A, where 4 0 -7 0 0 7 3 -6 3 -5 2 A = 4 -8 5 0 5 2 -3 0 0 9 -1 2…

A: To solve the following problem

Q: 6. Find the determinant of the 4x 4 matrix showing details of your work. 0 4 -1 -4 3 -2 1 -3 1 -5 2…

A:

Q: Consider the following matrix 3 1 -2 A = %3D -1 1 1 1 0 -1 a) By evaluating the determinant of A…

A:

Q: Solve the system of linear equations given below. -11х1 + 13х2 — 15хз + 25х4 %3D 101 -19x1 + 33x2 +…

A: Here is the solution

Q: 2 1 Let A = Show the details of two different methods [(1) using the 0 3 adjoint and determinant,…

A: I am attaching image so that you understand each and every step.

Q: 4. Evaluate the determinant of the matrix. 1.-4

A: The given matrix,              2-31-4

Q: 1 3 3 1 3 30 2 1 1 20 1 2 1 0 1 1 3 6 0 2 1 4 2 3 2 1 0 2 4 2 1

A: By Excel:

Q: 4. Determine whether the given matrix is invertible without computing its determinant. -3 0 1 3 5 8…

A:

Q: 2. Let A be the matrix 0 4 5. Suppose that B is a 3 x 3 matrix with det B = 2 (you are 0 0 6 not…

A: Given              A=123045006

Q: 3. Calculate the determinant of the matrix A using cofactor expansion. 1 3 4 0 10-32 A = 2 0 1 0 0 1…

A: Do the expansion of this given matrix along the second column to obtain the determinant by using the…

Q: 2. Use any method to evaluate the determinant of the given matrix. 1 0 0 0 1 0 0510 A = B = -2 8 3 0…

A: We have to find determinant of matrix A and B:

Q: 2 1 Let A = Show the details of two different methods [(1) using the adjoint and determinant, (2)…

A:

Q: Let A be a known nxn matrix, b be a known n-dimensional vector and z be an unknown vector defined by…

A: Given A is n×n b is a known n-dimensional vector and x be unknown vector defined by solution of Ax=b…

Q: 3.12. Let A be m x n and B be n x m matrices. Prove that A ) = det(AB). det -В I Hint: While it is…

A:

Q: - 1 3 -1 3 det(A - AI) det 2 1. |1 - i -1 - A 3 2 0 1- a To find the determinant, expand along the…

A: Let's find.

Q: 4. (a) Use row reduction to evaluate the determinant of the matrix, 3 -1 4 -1 1 5 В 3 2 1 2 [2 1 -3…

A: To find the determinant of the matrix using row reduction. Reduce the given matrix in row echelon…

Q: If the determinant of a 5×5 matrix A is det(A)=8, and the matrix C is obtained from A by swapping…

A: The determinant of a 5×5 matrix A is detA = 8 Formula Used: detC = -detA To evaluate: The value of…

Q: If a 4 x 4 matrix A with rows v1, v2, V3, and v4 has determinant det A = 4, %3D 4v1 + 5v2 7v1 + 9v2…

A: See the detailed solution below.

Q: If a 4 x 4 matrix A with rows v₁, U₂, U3, and 4 has determinant det A = 9, 5v₁ + 20₁ then det V2 U3…

A:

Q: 6

A:

Q: [2 11 Find the determinant of matrix -1 0 3 by using 1 2 0 (a) cofactor expansion, (b) properties of…

A:

Q: Evaluate the determinant of the given matrix by any legitimate method.

A: Given that, 1-23-12-512-1419-922-2031-49-1415

Q: 2. Considering matrix Č, [3 1 1 1 1 3 1 1 C = 1 1 3 1 |1 1 1 3 then provide step-by-step solution…

A: On interchanging any two rows or any two columns of a determinant, we get one negative sign one at a…

Q: 1 1 3 3 1 3 3 0 2 1 1 1 1 2 0 1 2 1 0 1 1 3 6 0 1 4 2 3 2 1 0 2 4 2 1

A: Using property 9 and  If we get a matrix B from a matrix A with Multiplying by c( non zero) to a…

Q: and the đesired inverse matrix i3 21 -7 1 6 31 -8 99 -9 |8| 3 12 You can check that the results in…

A:

Q: 1. Use the determinantal criterion for non-invertibility to find all the values of t for which the…

A:

Q: 2. If A is a 3 x 3 matrix, prove that the determinant of A is equal to the determinant of AT.

A: 2. Given A is a 3×3 matrix we need to show that determinant of A is equal to AT. Let A=abcdefghi.…

Q: Suppose that a 4 x 4 matrix A with rows v1, v2, v3, and v4 has determinant det A = 2. Find the…

A:

Q: 6. Suppose that a 3 x 3 matrix A has its three rows given by vectors u, v, and w in this order (that…

A: We need to solve Q 6 part a for which we will use the properties of determinant.

Q: Evaluate the determinant of the given matrix. det(A) = A² + 3x + 12 A²+ 3A - 10 x² + 3x + 2 A²+ 3A -…

A:

Q: 6. a) Find the determinant of matrix Q, where matrix Q = 4 -6 -7 0 5 1 3

A: Part a)

Q: 1. Combine the methods of row reduction and cofactor expansion to compute the determinant. 3 4 -3 -1…

A: The determinant is, 34-3-1301-3-60-4368-4-1To solve this determinant using combine method of row…

Q: In this question A is an n x n matrix. (a) State, and describe fully, a formula that allows the…

A: This given problem is related to linear algebra. Given: n × n matrix A. First, we have to find a…

Q: Evaluate the determinant of the given matrix by any legitimate method.

A: Given, A=i2-131+i2-2i14-i

Q: If the determinant of a 4 x 4 matrix A is det(A) = 5, and the matrix D is obtained from A by adding…

A:

Q: 1 3 1 -1 -7 1 -2 0 1 5 3 1 2.

A: solution  given below

Q: 4. Evaluate the determinant of the matrix by using a convenient column or row. (a) 3 -1 3 1 A = 2 0…

A:

Q: Evaluate the determinant of the given matrix by any legitimate method.

A: Given matrix, 10-23-311204-112301

Q: If the determinant of a 4×4 matrix A is det(A)=2, and the matrix D is obtained from A by adding 5…

A: Given det A= 2  D can be obtained by adding 5 times the third row to the second in A  See the…

Q: If the determinant of a 4 x 4 matrix A is det(A) = 7, and the matrix B is obtained from A by…

A:

Q: 30 2 1 11 1 2 0 1 2 1 0 113 6 0 2 1 4 2 3 2 1 0 2 4 2 1

A:

Q: [1 1 1] The qr-factorization of the 3 x 3 matrix B is QR where R = 0 2 2 0 0 3 absolute value of the…

A: If A∈Rm×n has linearly independent columns then it can be factor as A=QRwhere'Q is m×n…

Q: 1. Solve for the determinant of the following matrix. 1 2 3 4 3 2 0 -1 2

A: To find:det1234320-12

Q: 1. Choose three different non-zero integer values for the empty boxes and find the determinant of…

A: Let we assume three different non zero integers are 1,2 and 3

Q: 1. Find the determinant of the given matrix. 1 0 4 -6 2 5 3 -1 2 3 2 1 -2 31 det A

A: Given :A=104-62503-123521-23

Q: ) If the determinant of a 4 x 4 matrix A is det(A) = 10, and the matrix B is obtained from A by…

A: The objective is to find the determinant of B.

Q: Consider the following matrix 3 1 -2 A -1 1 1 1 0 a) By evaluating the determinant of A determine in…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.