EXAMPLE 4 Solve a matrix equation Solve the

EXAMPLE 4 Solve a matrix equation Solve the matrix equation for x and y. – 21 15 5 x – 2 3 7 3 + = 3 – 24 6 – 4 – 5 –y SOLUTION Simplify the left side of the equation. 3 5 x – 2 3 7 + 6 – 4 – 5 –y – 21 15 = 3 – 24 Write original equation.

EXAMPLE 4 3 Solve a matrix equation 5 – 4 – y – 21 15 = 3 – 24 Add matrices inside parentheses. 15 x + 9 15 3 – 12 – 3 y – 21 15 = 3 – 24 Perform scalar multiplication. 5 x + 3 1 Equate corresponding elements and solve the two resulting equations. 15 x + 9 = – 21 – 12 – 3 y = 224 x = – 2 y=4 ANSWER The solution is x = – 2 and y = 4.

GUIDED PRACTICE for Examples 3 and 4 5. In Example 3, find B – A and explain what information this matrix gives. ANSWER – 30 38 – 20 14 – 36 30 The difference in the number of DVD racks sold this month compare last month.

for Examples 3 and 4 GUIDED PRACTICE 6. Solve – 2 – 3 x 4 for x and y. ANSWER x = 5 and y = 6 – 1 y + 9 – 5 – 4 3 12 = 2 10 – 18

for Examples 3 and 4 GUIDED PRACTICE 7. Solve – 2 B = 12 2 10 -18 for B. ANSWER 12 ÷ (-2) 2÷ (-2) 10 ÷ (-2) -6 -18÷ (-2) = -1 -5 9

for Examples 3 and 4 GUIDED PRACTICE 8. Solve for A. ANSWER 12 10 2 – 18 A + 9 – 5 3 7 – 4 3 14 – 21 9 – 5 = – 4 3 12 = 2 10 – 18 12 - 9 10 – (-4) 2 - (-5) – 18 - 3