Question

What is the determinant of B? A. −27 B. −30 C. 30 D. –6

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Answer B:  -30

Step-by-step explanation:

Let B be as follows:

[-18 3]

[4    1 ]

To find the determinant, multiply diagonally downward from -18 through 1, obtaining -18.  We keep this sign as is.

Continue:  Start at 4 and move diagonally upward through 3; this product is 12. Because we moved upward, give this result the opposite sign:  -12.

Now add together these two products; that is, add together -18 and -12.  Here the sum is -30.  This is the determinant of the matrix.  It's Answer B.

Finding the determinant of a 3x3 matrix obviously requires more steps, but the general approach is similar.