Question

Help! I'm a little stumped when it comes to variables in matrices. An explanation would be super rad!

What is the determinant of A = [ -2 2 b 0 3 a 0 0 -5 ]

Answer 1

30

Explanation:

To find the determinant of a 3x3 matrix, you can use this method. (See picture.)

Start with the first number in the top row, and block off the row and column. A 2x2 matrix will be left. Find the determinant of this 2x2 matrix, and multiply it by the number in the top row.

Repeat for the other two numbers in the top row. Add the first result, subtract the second, and add the third.

det A = -2 [(3)(-5) − (a)(0)] − 2 [(0)(-5) − (a)(0)] + b [(0)(0) − (3)(0)]

det A = -2 (3)(-5) − 0 + 0

det A = 30