4.7 Solving Systems using Matrix Equations and Inverses
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Transcript of 4.7 Solving Systems using Matrix Equations and Inverses
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4.74.7Solving Systems using Solving Systems using Matrix Equations and Matrix Equations and
InversesInverses
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Matrix Equation
68
2145yx
A linear system can be written as a matrix equation AX=B
Coefficient matrix Variable
matrix
Constant matrix
5 4 81 2 6x yx y
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Ex. 1 Write as a matrix equation.
3 4 52 10x yx y
105
1243
yx
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Suppose ax = bHow do you solve for x?
We cannot divide matrices, but we can multiply by the inverse.
AX = BAA-1-1 AA-1-1
IX = AA-1-1BX = AA-1-1B
Solving Matrix Equations
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Ex. 2 Solve using matrices.
3 4 52 10x yx y
x = -7y = -4
105
1243
yx
A B
X = AA-1-1BAX = B
(-7, -4)
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Ex. 3 Solve using matrices7 3 1114 4 2x yx y
x = 5/7y = 2
(5/7, 2)
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Ex. 4 Solve using matrices2 3 13 3 12 4 2
x y zx y zx y z
x = 2y = -1z = -2
(2, -1, -2)
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Ex. 5 Solve using matrices
x y zx yx y z
3 5 152 19 8 4 12
x = 4y = -7z = 2
(4, -7, 2)
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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.
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Determine whether each system has an unique solution.
20x + 5y = 14530x – 5y = 125
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Assignment
Pg. 213 1-21 odd