SOLUTION: Find the inverse of the matrix, if it exists. [4 -2] [-5 5] I worked it out to: x=(4)(5)-(-2)(-2)=20-4=16 x^-1=1/16 matrix [5 2] and [5 4] on the bottom. What now?

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Question 189592This question is from textbook saxon algebra 2
: Find the inverse of the matrix, if it exists.
[4 -2]
[-5 5]
I worked it out to:
x=(4)(5)-(-2)(-2)=20-4=16
x^-1=1/16 matrix [5 2] and [5 4] on the bottom.
What now? This question is from textbook saxon algebra 2

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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

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