Step by step
The question
Question: find the determinant of this matrix.
D = |5, −6; 2, −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 = 5 × (−1) − 2 × (−6).
D = 5 × (−1) − 2 × (−6)
Careful!
The up product is −12, a negative number.
Taking it away is adding: −5 − (−12) = −5 + 12.
Careful: not −5 − 12 ✗
2 Down minus up
5 times (−1) is −5.
2 times (−6) is −12.
D = −5 − (−12)
Taking away a negative is adding: −5 + 12.
−5 − (−12) = −5 + 12
−5 minus (−12) is 7.
So D = 7.
D = 7
3 Check
Let's check the taking away by adding back: 7 + (−12) = −5, the down product.
So D = 7 is right!
7 + (−12) = −5
Let's look back.
First: multiply the diagonals.
Then: down minus up.
Last: check.
Answer
D = 7