SOLUTION: find inverse: *both matrices are 2x2. Rows separated by brackets* [[6,-3][7,9]]X=[[-18,-93][4,-21]] Please help. I have no idea how to do this.

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Question 982591: find inverse:
*both matrices are 2x2. Rows separated by brackets*
[[6,-3][7,9]]X=[[-18,-93][4,-21]]
Please help. I have no idea how to do this.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Find the inverse of the matrix

Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix , we can follow these steps:

Step 1) Find the determinant



The determinant of is . So this means that

Step 2) Swap the values



Now switch the highlighted values to get

Step 3) Change the sign



Now change the sign of the highlighted values to get

Step 4) Multiply by the inverse of the determinant



Multiply by to get

Plug in to get

Step 5) Multiply by every element in the matrix (simplify and reduce if possible)



Multiply by EVERY element to get

Multiply to get

Reduce each element:


=================================================================


Answer:

So the inverse of is

This means that if then



Now multiply both sides by the inverse matrix. The left side matrices will multiply to the identity matrix, leaving just matrix X behind.

On the right side, you will have to compute the matrix product to get the final answer for X
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