Det by row operations [0, 2; 3, 1]

Step by step

The question

Question: find the determinant by row operations of this matrix.

We call the rows R 1 and R 2.

1 The rules

Row moves change D in a known way.

A swap changes its sign.

A number taken out of a row goes in front.

Adding a multiple of one row to another changes nothing.

And with 0s under the diagonal, D is just the diagonal multiplied.

2 Get 0s under the diagonal

Careful!

The swap changed the sign of D.

Keep the minus in front, or the answer has the wrong sign.

3 Multiply the diagonal

The diagonal: 3 and 2.

Under it, all 0s.

So D is minus the diagonal multiplied: 3 × 2.

The diagonal makes 6.

So D = −6.

4 Check

Let's check with down minus up.

So D = 0 × 1 − 3 × 2.

0 times 1 is 0.

3 times 2 is 6.

0 minus 6 is −6.

So D = −6.

We get D = −6 again.

So the answer is right!

Let's look back.

First: the rules.

Then: get 0s under the diagonal.

Then: multiply the diagonal.

Last: check.