For each section, find the matrix X solving the given equation. [[0,0,1],[0,1,0],[1,0,0]]X = [[6,-6,-10],[-2,4,5],[-7,-2,-1]]

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embizze | High School Teacher | (Level 1) Educator Emeritus

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We are asked to solve the matrix equation AX=B for X. The solution is given by `A^(-1)B` since `A^(-1)AX=IX=A^(-1)B` .

We can find the inverse for matrix A using an algebra utility or Gauss-Jordan reduction of the augmented matrix.

Thus `A^(-1)=([0,0,1],[0,1,0,],[1,0,0])` and

`X=([0,0,1],[0,1,0],[1,0,0])([6,-6,-10],[-2,4,5],[-7,-2,-1])`

so `X=([-7,-2,-1],[-2,4,5],[6,-6,-10])`

Note that A exchanges rows I and III -- this is an example of an elementary transformation matrix.

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