7.6: The Inverse of a Square Matrix

ObjectivesSWBAT

•Use Gauss-Jordan elimination to find the inverse of matrices. •Use a formula to find the inverse of a 2x2 matrix. •Use inverse matrices to solve systems of linear equations

Vocabulary/Key Concepts

Inverse of a Square Matrix

Formula for Inverse of Matrix

Determinant of 2x2 Matrix

Inverse Matrix to Solve a System

Find the inverse of the matrix.

1. 1 2 3 7⎡

⎣⎢

⎤

⎦⎥

Find the inverse of the matrix.

2. 1 2 2 3 7 9−1 − 4 − 7

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

3. −8 0 11 −10⎡

⎣⎢

⎤

⎦⎥

Use the following formula to find the inverse of the 2x2 matrix.

A−1 =1

ad − bc

d − b −c a⎡

⎣⎢

⎤

⎦⎥A =

a b c d⎡

⎣⎢

⎤

⎦⎥

Use the following formula to find the inverse of the 2x2 matrix.

A−1 =1

ad − bc

d − b −c a⎡

⎣⎢

⎤

⎦⎥A =

a b c d⎡

⎣⎢

⎤

⎦⎥

4. 1 − 2−3 2⎡

⎣⎢

⎤

⎦⎥

5. x − 2y = 0 2x − 3y = 3

Use the given inverse matrix to solve the linear system of equations.

A−1 =−3 2−2 1⎡

⎣⎢

⎤

⎦⎥

6. x + y + z = −1 3x + 5y + 4z = 2 3x + 6y + 5z = 0

Use the given inverse matrix to solve the linear system of equations.

A−1 = 1 1 −1 −3 2 −1 3 − 3 2

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

7. x1 − 2x2 − x3 − 2x4 = 1 3x1 − 5x2 − 2x3 − 3x4 = −2 2x1 − 5x2 − 2x3 − 5x4 = 0 − x1 + 4x2 + 4x3 +11x4 = −3

Use the calculator to find the inverse matrix and solve the system of linear equations.