1. Compute the determinant using a cofactor expansion across the first row.-1 2-7 1-3 23522. Compute the determinant using a cofactor expansion down the second column.2 -112(a)3 -11 11More problems: 5-8 section 3.13. Compute the determinants by cofactor expansion. At each step, choose a row or column that involvesthe least amount of computation.(a)0210011 5 80 10 05 781704. Find the determinants by row reduction to echelon form.2 -1 41 3 -12 1 11O co00∞ W NO230 6 020(b)87 0 20 3-25 7 8More problems: 5-10 section 3.25. Combine the methods of row reduction and cofactor expansion to compute the determinants.0 -7 -52310660More problems: 1-4 section 3.11-20 0 22-6 71 4 -45 215-2 6670 7 3200 11800 2 1More problems: 9-14 section 3.1(c)More problems: 11-14 section 3.2

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Answered: 1. Compute the determinant using a…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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2(6) find the determinant of the given elementary matrix by inspection.
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)?
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.
From the given matrix A. 1. What is the determinant of A along the second column? (Use cofactor expansion)2. Determine (A - 2I3)3 .
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)=
Suppose A is a 5 by 5 matrix. Its entries in row 1 multiply determinants (cofactors) in rows 2-5 to give the determinant. Can you guess a "Jacobi formula" for det A using 2 by 2 determinants from rows 1-2 times 3 by 3 determinants from rows 3-5? Test your formula on the -1, 2, -1 tridiagonal matrix that has determinant= 6.
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.
2. Let A be any 4 ×4 matrix. Compute the determinant of the appropriate elementary matrix to prove each of the following. a. Swapping Row 1 and Row 3 causes the determinant to change sign. b. Replacing Row 3 by (Row 3 - 2*Row 2) does not change the determinant.
1.If A is 4x4 matrix with det(A)=10, find det ( 2? ^-1 ?^? ), det ( ?^2) 2. Use determinant to find the equation of the line that passes through the points (4, ― 3)& ( ―1,2)
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(?)=
1. Use determinants to find x, y, and z in the below equations:
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(?)=

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