Step by step
The question
Question: find the determinant of this matrix.
D = |3, −2; −4, 1|
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 = 3 × 1 − (−4 × (−2)).
D = 3 × 1 − (−4 × (−2))
Careful!
Always down minus up.
Up minus down gives the wrong sign.
Careful: not 8 − 3 ✗
2 Down minus up
3 times 1 is 3.
−4 times (−2) is 8.
D = 3 − 8
3 minus 8 is −5.
So D = −5.
D = −5
3 Check
Let's check the taking away by adding back: −5 + 8 = 3, the down product.
So D = −5 is right!
−5 + 8 = 3
Let's look back.
First: multiply the diagonals.
Then: down minus up.
Last: check.
Answer
D = −5