4.7 Solving Systems using Matrix Equations and Inverses

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Presentation transcript:

4.7 Solving Systems using Matrix Equations and Inverses

Matrix Equation A linear system can be written as a matrix equation AX=B Constant matrix Coefficient matrix Variable matrix

Ex. 1 Write as a matrix equation.

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

Ex. 2 Solve using matrices. AX = B X = A-1B A x = -7 y = -4 B (-7, -4)

Ex. 3 Solve using matrices y = 2 (5/7, 2)

Ex. 4 Solve using matrices y = -1 z = -2 (2, -1, -2)

Ex. 5 Solve using matrices y = -7 z = 2 (4, -7, 2)

Unique Solutions Find detA. If it = 0 then there is an unique solution. If detA = 0 then the system does not have a unique solution.

Determine whether each system has an unique solution. 20x + 5y = 145 30x – 5y = 125

Assignment Pg. 213 1-21 odd