4'5 Solving Systems using Matrix Equations and Inverses

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4.5Solving Systems using Matrix Equations and
Inverses
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Matrix Equation
A linear system can be written as a matrix
equation AXB
Constant matrix
Coefficient matrix
Variable matrix
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Ex. 1 Write as a matrix equation.
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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
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Ex. 2 Solve using matrices.
AX B
X A-1B
x -7 y -4
B
A
(-7, -4)
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Ex. 3 Solve using matrices
x 5/7 y 2
(5/7, 2)
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Ex. 4 Solve using matrices
x 2 y -1 z -2
(2, -1, -2)
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Ex. 5 Solve using matrices
x 4 y -7 z 2
(4, -7, 2)
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Assignment