SOLUTION: Solve for Matrix X: {{{(matrix(2,2,-3,-14,2,9))X=(matrix(2,2,8,-4,0,-4))}}}

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve for Matrix X: {{{(matrix(2,2,-3,-14,2,9))X=(matrix(2,2,8,-4,0,-4))}}}      Log On


   

Question 173474: Solve for Matrix X:
%28matrix%282%2C2%2C-3%2C-14%2C2%2C9%29%29X=%28matrix%282%2C2%2C8%2C-4%2C0%2C-4%29%29
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!


%28matrix%282%2C2%2C-3%2C-14%2C2%2C9%29%29X=%28matrix%282%2C2%2C8%2C-4%2C0%2C-4%29%29

First find the inverse of %28matrix%282%2C2%2C-3%2C-14%2C2%2C9%29%29 by

1. find the determinant 



2. Swap the elements is the upper left to lower right diagonal.
   Change the signs in the other diagonal.

%28matrix%282%2C2%2C-9%2C14%2C2%2C3%29%29


3. Divide the matrix through by the determinant

 

That is the inverse matrix. So left-multiply both sides
of the original equation by this inverse:

%28matrix%282%2C2%2C-3%2C-14%2C2%2C9%29%29X=%28matrix%282%2C2%2C8%2C-4%2C0%2C-4%29%29




%28matrix%282%2C2%2C1%2C0%2C0%2C1%29%29X=%28matrix%282%2C2%2C-72%2C-20%2C16%2C-20%29%29

X=%28matrix%282%2C2%2C-72%2C-20%2C16%2C-20%29%29

Edwin