Exercise 5 Page 194

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. 3*(2)* 4 &= 24 -2* (-5) *( -3) &= -30 2*( -4)* 1 &= -8

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. -3*2* 2 &= -12 1* (-5) * 3 &= -15 4*( -4)* (-2) &= 32

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.

[ 24+( -30)+( -8)]-[ -12+( -15)+ 32]

AddNeg

a+(- b)=a-b

[24-30-8]-[-12-15+32]

SubTerms

Subtract terms

-14-5

SubTerm

Subtract term

-19