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?

Algebra ->  College  -> Linear Algebra -> 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?      Log On


   

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) About Me  (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 A=%28matrix%282%2C2%2C4%2C-2%2C-5%2C5%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C4%2C-2%2C-5%2C5%29%29 is abs%28matrix%282%2C2%2C4%2C-2%2C-5%2C5%29%29=10. So this means that d=10

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%284%29%2C-2%2C-5%2Chighlight%285%29%29%29 to get %28matrix%282%2C2%2Chighlight%285%29%2C-2%2C-5%2Chighlight%284%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C5%2Chighlight%28-2%29%2Chighlight%28-5%29%2C4%29%29 to get %28matrix%282%2C2%2C5%2Chighlight%282%29%2Chighlight%285%29%2C4%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C5%2C2%2C5%2C4%29%29

Plug in d=10 to get %281%2F10%29%28matrix%282%2C2%2C5%2C2%2C5%2C4%29%29

Step 5) Multiply 1%2F10 by every element in the matrix (simplify and reduce if possible)



Multiply 1%2F10 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C5%2F10%2C2%2F10%2C5%2F10%2C4%2F10%29%29

Reduce each element: %28matrix%282%2C2%2C1%2F2%2C1%2F5%2C1%2F2%2C2%2F5%29%29


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


Answer:

So the inverse of %28matrix%282%2C2%2C4%2C-2%2C-5%2C5%29%29 is %28matrix%282%2C2%2C1%2F2%2C1%2F5%2C1%2F2%2C2%2F5%29%29

This means that if A=%28matrix%282%2C2%2C4%2C-2%2C-5%2C5%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C1%2F2%2C1%2F5%2C1%2F2%2C2%2F5%29%29