Answered: Problem 4. Evaluate the determinant by…

Problem 4. Evaluate the determinant by expanding along the row or column that minimize the amount of computation that is required. 0 -2 6 -7 -1 3 4 8 8 4 3 -2 O5070

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.1: The Determinants Of A Matrix

Problem 70E: The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six...

See similar textbooks

Related questions

Q: Problem No.4 Evaluate the determinants of the following matrices using cofactor expansion method: 1…

A: Solution: Find determinant using cofactor: a) A=23-104200-5 b) B=1-213-2508-1 c) C=1-λ1-32λ00-4-2-λ…

Q: Problem 1: Let A be a 4 x 4 matrix and suppose that |A| = 8. Using properties of determinants and…

Q: Think Diagonal Usethe ideas of Problem 15 to evaluate the determinants in Problems 16–19. -3 4 0 0 7…

Q: Problem 2. Give an explicit example for each part. If no such example exists, write “DNE".…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Question 2 Calculate the determinant of the matrix by choosing the third row as the center. 3 -4 -1…

A: Determine of A by choosing thrid row as the centre.

Q: Question 3 Find the determinant of the matrix 4 0 -7 3 -5 7 3 -6 4 -8 5 0 -3 0 0 9 -1 2 2.

A: 40-73-50020073-64-85052-3009-12

Q: If the determinant of a 4 x 4 matrix A is det(A) = 9, and the matrix D is obtained from A by adding…

Q: Question 21 Find the determinant of the matrix 6 0 0 17 2 -5 5 2 0 8 3 1 8 A -10 B) -5 D 10

Q: of [ $ Example 29 a If the determinant of 5-3 3 is equal to 21, what is the value of x?

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Problem #13: Find the determinant of the following huge matrix. 0 0 0 0 0 0 0 0 0 6 0 0 1 0 1 1 5 -7…

A: The given matrix is…

Q: Question 9 If A is a 5x5 invertible matrix, then the determinant of 2A is k|A| where k is equal to A…

Q: Problem (1) Find the determinant of the following matrix using Arrow Method 1 1 20 -1 3 0 2 1

Q: In Problems 26–28, find the value of each determinant. |2 1 28. 5 0 2 6 1 4 0 -3 3 4 26. 1 27. -1 2…

A: The given matrix is 3413

Q: Problem 1: Let A be a 4 x 4 matrix and suppose that |A| = 8. Using properties of determinants and…

Q: 1. Compute the determinant using a cofactor expansion across the first row. 3 -1 2 5 -7 1 2-3 2 2.…

Q: Question 2 (i) Find the determinant of the matrix 1 4 -3 6. -4 (ii) Test the constituency of the…

A: Answer(a):

Q: Find the Properties State which one of the row operations for determinants is illustrated in each of…

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: SITUATION 5: From the given matrix, use f42 as the pivot +3 -2 +2 -3 +5 -2 -3 4 F = +3 -4 -1 l+4 +1…

A: Given matrix: F=23-20-2-34-33-4-1541-35 Taking f42=1 as the pivot, the determinant using Chio's…

Q: Problem 1 (20 points). Find the determinant of matrix A. A = 5 2 4 40-7 07 5 ∞ Ne 51 2 30 8

Q: 1. Find the determinant by row reduction to echelon form. 1 -3 0 5 4 1 1 -1 5 3 3 -3 -2 3

Q: Find the values of A for which the determinant is zero. a+1 0 4 4 2 6 A+5)

Q: 5. Use a determinant to find the values of x for which the matrix below is singular. (3 2 4 A = (2 0…

Q: Problem 1 Let the matrix A be given by 34 A = 1 1 -1 1 2 a) Calculate the determinant of A. b)…

Q: Question 9 Find the determinant of 5 -7 2 3 0 -4 -5 -8 3 5 0 -6 A) 10 B) -20 -10 D) 20

Q: Question Five: Find the determinant of the matrix [1 2 A = 3 7 l1 -1] 0 -1 -1 6

Q: In Problems 17 and 18, find the value of each determinant. 2 -4 6. 2 5 3 7 17. 18. 1 4 -1 2 -4

A: given, 17. -253718. 2-4614012-4

Q: Find the determinant of the following matrix 1 -6 2 1 2 1 1 -2 1 3 | 2 1 2 1 M 3 8 0. 0. -1 0

Q: Problem 7 Let A be a (6x6) matrix such that the dimension of its column space is 6. Then Select all…

A: Note: According to our guidelines we can answer only first question 7

Q: Problem 1 Let the matrix A be given by 2 3 4 2 1 1 1 2 A = a) Calculate the determinant of A. b)…

A: Determinant of a Matrix: To every square matrix A = [aij] of order n, we can associate a number…

Q: Problem 1. Compute the determinant of the given matrix shown below. 4 -1 2 3 1 2 2 1 4 |A|= |10 3 1…

Q: If the determinant of a 5 x 5 matrix A is det(A) = 9, and the matrix B is obtained from A by…

A: If A is n×n matrix then det(aA)= andet(A). Just use this property of determinant of a matrix and…

Q: Problem 1: Consider the following two square matrices A=[2345], B=[5−32−6] Find A + B and A-2B…

A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

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: 2. If the determinant of a 5×5 matrix A is det(A)=6, and the matrix C is obtained from A by swapping…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 4. Find the determinants by row reduction to echelon form. (a) 2 -1 4 1 3 -1 2 1 11 0 2 3 1 0 0 6 6…

Q: Question 10 [1 2 3 Which of the following is equivalent to the determinant of 4 5 6 7 8 9 O 5 6 2 3…

Q: Problem 2: Solve the following simultaneous equations using Cramer's Rule. Show all steps including…

A: Given: Given system of linear equations are 25x1-5x2-20x3=50-5x1+10x2-4x3=0-5x1-4x2+9x3=0 We want…

Q: Question 10 Find the determinant of the matrix 3 -4 4 1 A 15 B -23 C) -17

Q: Question 3 Compute the determinant of the matrix by Gaussian elimination. Although these are…

Q: Problem 2 Find the following determinants: 0.4 2 -1 - 0.5 3 - 1 -1 5 12 |-1.2 -6 3 1.5 -9 17 19 3.7…

A: Given determinant is 0.42-1-0.531-10512-1.2-631.5-917193.71520325.68.713

Q: Problem 1: Use the elementary row or column operations AND cofactor method to find the determinant.…

Q: Question 23 Find the determinant of the matrix 3 2 4 0 9 0 -4 6 7 1 -5 1 3 2 3 2 A 9. в) 5 6.

Q: Problem 2. Consider the following linear system: xi+ 2x2 + x3 -2x1 – 12 – 13 4x1 + 3x2 – 13 %3D -1.…

A: Given system of equations are x1+2x2+x3=3-2x1-x2-x3=-14x1+3x2-x3=-3solve the given system of…

Q: Problem 7 Let A be a (13x13) matrix such that the dimension of its column space is 13. Then Select…

Q: Question 18 Find the determinant of the matrix 1 -2 5 2 3 2 -6 -7 4 A 6. B. 3. -6 D. 3.

Q: Problem No.2 Evaluate the determinant of the given matrix A= 1 3 4 -1 1 -1 4 0 1 -1 1 2 2 -1 3 2

Q: Question 16 Find the determinant of 1 3 -1 0 - 2 -4 -1 -6 -2 -6 9. 3 7 -3 -7 3 5 2 7 A) 24 в) 12 -24…

A: We need to calculate the determinant.

Q: The following problem illustrates a danger that occurs because of round-off error when nearly equal…

Q: Problem 15. Compute the determinants of the following matrice [123] (a) A = (b) B = (c) C = -- 1 1 1…

A: Lets find the determinants of the below matrices det A=|ad-bc|

Question

Problem 4. Evaluate the determinant by expanding along the row or column that
minimize the amount of computation that is required.
0 -2
6 -7
-1
3
4
8.
2
8.
7 -6
4
3 -2
O 5 O o

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Determinant$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The 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.
2. If the determinant of a 5×5 matrix A is det(A)=6, and the matrix C is obtained from A by swapping the second and third rows, then what is det(C)? 3. If the determinant of a 4×4 matrix A is det(A)=8, and the matrix D is obtained from A by adding 2 times the fourth row to the first, then what is det(D)?
1. If the determinant of a 5×5 matrix A is det(A)=9, and the matrix B is obtained from A by multiplying the first row by 8, then what is det(B)? 2. If the determinant of a 5×5 matrix A is det(A)=6, and the matrix C is obtained from A by swapping the second and third rows, then what is det(C)? 3. If the determinant of a 4×4 matrix A is det(A)=8, and the matrix D is obtained from A by adding 2 times the fourth row to the first, then what is det(D)? 4. If A and B are 2×2= matrices, det(A)=5, det(B)=4, theni. det(AB)= ii. det(−3A)= iii. det(A^T)= iv. det(B^−1)= v. det(B^2)=
Problem 1: Consider the following two square matrices A=[2345], B=[5−32−6] Find A + B and A-2B Find the products AB and BA. Is AB = BA, why or why not? Is A a singular matrix, why or why not? Problem 2: Find the determinant of A, that is |A|, if A=⎡⎢⎣230−15−3042⎤⎥⎦Problem 3: Find the determinant of AT, that is |AT|, using Matrix A defined in problem 2 aboveProblem 4: Find the inverse of a 2 X 2 matrix B defined in problem 1 above
If the determinant of a 4×4 matrix A is det(A)=2, and the matrix D is obtained from A by adding 5 times the third row to the second, thendet(?)=
If the determinant of a 5×5 matrix A is det(A)=8, and the matrix C is obtained from A by swapping the third and fourth rows, thendet(?)=
2(6) find the determinant of the given elementary matrix by inspection.
If the determinant of a 3×3 matrix A is det(A)=2, and the matrix B is obtained from A by multiplying the first column by 3, thendet(B)=
. Prove that,if row 2 of a 3 by 3 determinant is multiplied by k,k ≠0, and the result is added to the entries in row 1, there is no change in the value of the determinant.
The following problem illustrates a danger that occurs because of round-off error when nearly equal numbers are subtracted and the difference is then multiplied by a large number. Evaluate the quantity 1000⋅∣∣∣6.01018.042.0046.000∣∣∣1000·6.01018.0402.00416.000 in the following ways: a.First round each entry in the determinant to two digits. b.First round each entry in the determinant to three digits. c.Retain all four digits. Compare this value with the results in parts a and b.
Show that the elimination method of computing the value of the determinant of an n × n matrix involves [n(n − 1)(2n − 1)]/6 additions and [(n − 1)(n2 + n + 3)]/3 multiplications and divisions. Hint: At the ith step of the reduction process, it takes n − i divisions to calculate the multiples of the ith row that are to be subtracted from the remaining rows below the pivot. We must then calculate new values for the (n − i)2 entries in rows i + 1 through n and columns i + 1 through n.
40 - Which of the following is the definition of the determinant of the coefficients of the system of linear equations of order n. a) It is the determinant created by placing the constants on the right side of the system instead of the second column elements in the coefficients determinant. B) It is the determinant formed from the coefficients of the unknowns. NS) It is the determinant created by placing the constants on the right side of the system instead of the fifth column elements in the coefficients determinant. D) It is the determinant created by placing the constants on the right side of the system instead of the first column elements in the coefficients determinant. TO) It is the determinant created by placing the constants on the right side of the system instead of the last column elements in the coefficients determinant.