# EXAMPLE 2 Solve a matrix equation SOLUTION Begin by finding the inverse of A. 4 7 1 2 = Solve the matrix equation AX = B for the 2 × 2 matrix X. 2 –7 –1.

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EXAMPLE 2 Solve a matrix equation SOLUTION Begin by finding the inverse of A. 4 7 1 2 = Solve the matrix equation AX = B for the 2 × 2 matrix X. 2 –7 –1 4 –21 3 12 –2 A B X = A –1 = 1 8 – 7 4 7 1 2

EXAMPLE 2 Solve a matrix equation To solve the equation for X, multiply both sides of the equation by A – 1 on the left. A –1 AX = A –1 B IX = A –1 B X = A –1 B X = 0 –2 3 –1 4 7 1 2 –21 3 12 –2 = 2 –7 –1 4 4 7 1 2 X X 1 0 0 1 0 –2 3 –1 =

GUIDED PRACTICE for Example 2 4. Solve the matrix equation –4 1 0 6 X = 8 9 24 6 –1 –2 4 1 ANSWER

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