Question

Evaluate the determinant.

-3 5 -2
3 0 -3
3 0 1

A. 60

B. -30

C. -60

D. 30

Answer 1

@Hero

Answer 2

-3 5 -2
3 0 -3
3 0 1

Add R1 to R2:

-3 5 -2
0 5 - 5
3 0 1

Reduce matrix A to a 2 x 2 matrix:

-15 -15
-15 5

Reduce to 1 x 1 matrix:

-300

Divide by the interior of matrix A:
-300/5 = -60

Thus the determinant of the matrix is -60

Answer 3

wow, thank you so much!

Answer 4

Did you understand the steps?

Answer 5

yes, I appreciate you explaining it so well.

Answer 6

For example, do you understand how I reduced matrix A to a 2 x 2 matrix?

Answer 7

Or why I needed to add R1 to R2?

Answer 8

yes, I understand. I just mixed up a negative sign when working it out so I needed to double check.

Answer 9

So how did I come up with the 2 x 2 matrix? Explain...

Answer 10

Multiply the three numbers on the diagonal from the first row and first column number to the third row and third column number.

Answer 11

???

Answer 12

No, that's not how it was done.

Answer 13

you look at the first number in each row, and decide what factor of Row 1 needs to be added/subtracted from each row to get zero as the first term.