Question

Let A be a 4×4 matrix and suppose that det(A)=3. For each of the following row operations, determine the value of det(B), where B is the matrix obtained by applying that row operation to A. a) Add 4 times row 4 to row 3 b) Multiply row 3 by 3 c) Interchange rows 1 and 4 Resulting values for det(B):

Answer 1

Answer:

a)3

b) 9

c) -3

Step-by-step explanation:

a) If B is obtained by adding a multiple of a row of A to another row of A, $det (B) = det (A).$

Then, $det(B)=3$.

b) If B is obtained by multiplying a row of A by k, then $det (B) = kdet (A)$. Then $det(B)=3det(A)=3*3=9$

c) If B is obtained by exchanging two rows (columns) of A, then $det (B) = - det (A)$. Then $det (B) = - 3$