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# Solving a matrix equation to find X?

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Hello everyone. It's GenericUsernameHere again. It's been a long time. I need some help with a review problem that I can't figure out. I'm not logged in because I can't remember my password. Please help.

[4 -3 6]         [18]

[-1 5 4] * X = [48]

[6 -2 5]         [0]

Guest May 16, 2017
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Define  A   as

[ 4 - 3  6  ]

[ -1  5  4  ]

[6  -2   5  ]

Define b  as

[18]

[48]

[0]

And

Ax  = b

Multiply on the left by the inverse of A  = A-1

(A-1 * A)  x  =  (A-1 ) b

x  =  ( A-1 )  b

The inverse of A  is

-11/41    -1/41    14/41

-29/123  16/123  22/123

28/123    10/123   -17/123

So   (A-1) * b   =   x

-11/41    -1/41    14/41                         18                 -6

-29/123  16/123  22/123           *          48        =       2

28/123    10/123   -17/123                    0                   8

So  x   =      -6

2

8

CPhill  May 16, 2017

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