Exercise 62 Page 970

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 upper-right 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. 1* 2* (- 4) &= - 8 3* 1 *( - 2) &= - 6 (- 1)* 1*( - 5) &= 5

Step 3

We will repeat the previous step, but draw diagonals beginning with the upper-right number.

As we did before, let's multiply the numbers in each diagonal. - 2* 2*(- 1) &= 4 - 5* 1 * 1 &= - 5 (- 4)* 1* 3 &= - 12

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.

[ - 8+( - 6)+ 5]-[ 4+( - 5)+( - 12)]

AddNeg

a+(- b)=a-b

[- 8-6+5]-[4-5-12]

AddSubTerms

Add and subtract terms

[- 9]-[- 13]

SubNeg

a-(- b)=a+b

4

This corresponds to option I.