Use Inverse Matrices to Solve Linear Systems

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Presentation transcript:

Use Inverse Matrices to Solve Linear Systems Notes 3.8 (Day 1) Use Inverse Matrices to Solve Linear Systems

The inverse of the matrix is

Find the inverse of:

Find the inverse of:

Find the inverse of:

Find the inverse of:

Identity matrix A matrix with 1’s on the main diagonal and 0’s elsewhere. 2 x 2 Identity Matrix 3 x 3 Identity Matrix Just like the identity property of multiplication (anything times 1 is itself), in matrix algebra any matrix multiplied by the identity matrix is itself.

Solving matrix equations AX = B for the 2 x 2 matrix X. Step 1: Find the inverse of A. Step 2: Multiply both sides of the equation by the inverse of A. Step 3: The identity matrix should appear on the left hand side of the equation, and on the right should be a 2 x 2 matrix. Step 4: In matrix multiplication, anything multiplied by the identity matrix is itself. Step 5: The solution is the remaining 2 x 2 matrix on the right hand side of the equation.

Solve the matrix equation AX = B for the 2 x 2 matrix X.

Solve the matrix equation AX = B for the 2 x 2 matrix X.

Solve the matrix equation AX = B for the 2 x 2 matrix X.

Homework: P 214 3-10, 13-18