2.3/3.1/3.2

Question 1

what is co factor expansion?

Answer 1

a formula for calcing the det A using cofactors associated with one row or one column, such as for row 1: det A = a_11*C_11 + …. + a_1n * C_1n

Question 2

what are the row operations on a square matrix?

Answer 2

a. if a multiple of one row of A is added to another to produce a matrix B, then det B = det A
b. if 2 rows of A are interchanged to produce B, then det B = -det A
c. if one row of A is multiplied by k to produce B, then det B = k * det A.

Question 3

if you’re trying to find the det of a matrix using row operations and you end up with a row of all zeros?

Answer 3

the matrix is linearly dependent and the det of the matrix is 0.

Question 4

if A is an n x n matrix, then det A^T

Answer 4

equals det A

Question 5

whats the multiplicative property for determinants

Answer 5

If A and B are n x n matrics, then det AB = (det A)(det B)

Question 6

what must the det be of a square matrix iff it’s invertible?

Answer 6

det A ≠ 0

Question 7

T or F: det(A)^-1 = ​(-​1)det A

Answer 7

The statement is false. det(A)^-1 = (det A)^​(-​1)

Question 8

Find a formula for det(rA) when A is an n x n matrix.

Answer 8

det(rA) = r^n * det A