Exercise 29 Page 195

To evaluate the determinant of a 3* 3 matrix, we use the diagonal rule.

1. Rewrite the first two columns to the right of the determinant.
2. Draw diagonals, beginning with the upper-left number. Multiply the numbers in each diagonal.
3. Repeat the second step, this time beginning with the bottom-left number.
4. Find the sum of the products of the numbers in each set of diagonals, and subtract the second sum from the first.

Let's do it!

Step 1

We will write the given determinant and copy the first two columns on the right-hand side.

Step 2

Now, we will draw diagonals beginning with the upper-left number.

Let's multiply the numbers in each diagonal. 3*(- 4)* 5 &= - 60 5* 6 *( - 6) &= - 180 - 2*( - 1)*(- 2) &= - 4

Step 3

We will repeat the previous step, but draw diagonals beginning with the bottom-left number.

As we did before, let's multiply the numbers in each diagonal. - 6*(- 4)*(- 2) &= - 48 - 2* 6 * 3 &= - 36 5*( - 1)* 5 &= - 25

Step 4

Finally, we will find the sum of the products in each set of diagonals. Then we will subtract the second sum from the first sum.