Det [-2, -1; 3, -4]

Step by step

The question

Question: find the determinant of this matrix.

The determinant is one number we get from a square matrix.

We write the matrix between two straight lines, and call it D.

1 Multiply the diagonals

So D = −2 × (−4) − 3 × (−1).

Careful!

The up product is −3, a negative number.

Taking it away is adding: 8 − (−3) = 8 + 3.

2 Down minus up

−2 times (−4) is 8.

3 times (−1) is −3.

Taking away a negative is adding: 8 + 3.

8 minus (−3) is 11.

So D = 11.

3 Check

Let's check the taking away by adding back: 11 + (−3) = 8, the down product.

So D = 11 is right!

Let's look back.

First: multiply the diagonals.

Then: down minus up.

Last: check.