14.6
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14.6. Solving Systems of 3 or More Variables. Why a Matrix?. In previous math classes you solved systems of two linear equations using the following method: Graphing Substitution Elimination. - PowerPoint PPT PresentationTRANSCRIPT
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Solving Systems of 3 or More Variables
14.6
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Why a Matrix?
• In previous math classes you solved systems of two linear equations using the following method:• Graphing
• Substitution
• Elimination
• These solutions were 2-dimensional (x, y). Matrices can also be used to solve systems of equations. They are especially useful in systems that involve 3 or more variables.
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We Live in a 3 Dimensional World, … Right?
• Add the following points to the graph• (3, 4, 0)and (3, 4, -2)
Look carefully at the example of graphing the 3 dimensional point (3,2,4).
Where x=3, y=2, and z=4
(3 ,4 ,0)(3 ,4 ,−2)
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Solve by hand { −𝑥+𝑦 +2𝑧=32 𝑥− 𝑦+𝑧=3
−5 𝑥+2 𝑦+3 𝑧=4
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Using a Matrix to solve
• First: Split the system into 3 matrices:
• Matrix A holds the coefficients
• Matrix X holds the variables• This matrix is called the vector matrix.
• Matrix B hold the integer values to the right of the = sign.
Ex 2:
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Sove for
• To solve for “X”, we need to isolate matrix X by simplifying matrix A to “1” in matrix form.• We do this by multiplying Matrix A
by it inverse matrix
• So…to solve a system of equations using matrices we use:
Now Solve example 2 again, this time using a matrix and your calculator. [ 𝐴 ]−1 [ 𝐴 ] [ 𝑋 ]= [𝐴 ]− 1 [𝐵 ]
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Now you try…
Aren’t you glad you aren’t doing this by hand?