SOLUTION: Fine the inverse matrix of A=2 -4 , find A^-1 -2 5 Can someone please help me and show all steps? Thanks

Algebra ->  Matrices-and-determiminant -> SOLUTION: Fine the inverse matrix of A=2 -4 , find A^-1 -2 5 Can someone please help me and show all steps? Thanks       Log On


   

Question 588527: Fine the inverse matrix of A=2 -4 , find A^-1
-2 5

Can someone please help me and show all steps?
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help with finding the inverse of 2x2 matrices, check out this solver


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

To find the inverse of the matrix A=%28matrix%282%2C2%2C2%2C-4%2C-2%2C5%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C2%2C-4%2C-2%2C5%29%29 is abs%28matrix%282%2C2%2C2%2C-4%2C-2%2C5%29%29=2. So this means that d=2

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%282%29%2C-4%2C-2%2Chighlight%285%29%29%29 to get %28matrix%282%2C2%2Chighlight%285%29%2C-4%2C-2%2Chighlight%282%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C5%2Chighlight%28-4%29%2Chighlight%28-2%29%2C2%29%29 to get %28matrix%282%2C2%2C5%2Chighlight%284%29%2Chighlight%282%29%2C2%29%29

Step 4) Multiply by the inverse of the determinant



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

Plug in d=2 to get %281%2F2%29%28matrix%282%2C2%2C5%2C4%2C2%2C2%29%29

Step 5) Multiply 1%2F2 by every element in the matrix (simplify and reduce if possible)



Multiply 1%2F2 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C5%2F2%2C4%2F2%2C2%2F2%2C2%2F2%29%29

Reduce each element: %28matrix%282%2C2%2C5%2F2%2C2%2C1%2C1%29%29


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


Answer:

So the inverse of %28matrix%282%2C2%2C2%2C-4%2C-2%2C5%29%29 is %28matrix%282%2C2%2C5%2F2%2C2%2C1%2C1%29%29

This means that if A=%28matrix%282%2C2%2C2%2C-4%2C-2%2C5%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C5%2F2%2C2%2C1%2C1%29%29