1. 1.11 Use Inverse Matrices to Solve Linear Systems
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2. Matrix Equation
A linear system can be written as a matrix equation AX=B
Constant matrix
Coefficient matrix
Variable matrix

3. Ex. 1 Write as a matrix equation.

4. Solving Matrix Equations
Suppose Ax = B
How do you solve for x?
We cannot divide matrices, but we can multiply by the inverse.
A-1
Ax = B
A-1
Ix = A-1B
x = A-1B
Conclusion: X = the inverse of A times B.

5. Solving a Matrix Equation
Solve the matrix equation Ax=B for the 2x2 matrix

6. Step 2: Multiply both sides of the equation
Step 1: find A-1
A-1=
Step 2: Multiply both sides of the equation
By A-1 on the left

7. You can check the Solution by mult AX to see if you get B
From Previous Slide
You can check the
Solution by mult
AX to see if you get B

8. Ex. Solve

9. Solve the Following System of Equations

10. Assignment
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