SOLUTION: find the inverse of matrix. 1. {{{(matrix(2,2,2, -1, 10, 7))}}} 2. {{{(matrix(2,2,-4,2, -5, 1))}}} 3. {{{(matrix(2,2,9, -3, -6, 2))}}}

Algebra ->  Matrices-and-determiminant -> SOLUTION: find the inverse of matrix. 1. {{{(matrix(2,2,2, -1, 10, 7))}}} 2. {{{(matrix(2,2,-4,2, -5, 1))}}} 3. {{{(matrix(2,2,9, -3, -6, 2))}}}       Log On


   

Question 172008: find the inverse of matrix.

1. %28matrix%282%2C2%2C2%2C+-1%2C+10%2C+7%29%29
2. %28matrix%282%2C2%2C-4%2C2%2C+-5%2C+1%29%29
3. %28matrix%282%2C2%2C9%2C+-3%2C+-6%2C+2%29%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

5-step rule for finding the inverse of a 2x2 matrix:

Step 1. Find the determinant by finding the difference
between the product of the elements on the
upper left to lower right diagonal, and the 
product of the elements on the upper left to 
lower right diagonal.  If this determinant is 0,
then the matrix has no inverse and is said to
be "singular".

Step 2. Swap the elements in the upper left to lower right
diagonal.

Step 3. Change the signs of the upper right to lower left
diagonal elements.

Step 4. Divide every element by the determinant value
fund in step 1.

Step 5. Reduce if possible.
 
Matrix 1. %28matrix%282%2C2%2C2%2C+-1%2C10%2C+7%29%29
Step 1. Find the determinant by finding the difference
between the product of the elements on the
upper left to lower right diagonal, and the 
product of the elements on the upper left to 
lower right diagonal.   If this determinant is 0,
then the matrix has no inverse and is said to
be "singular".

determinant+=+%282%29%287%29-%28-1%29%2810%29+=+%2814%29-%28-10%29+=+14%2B10+=+24     

Step 2. Swap the elements in the upper left to lower right
diagonal.

%28matrix%282%2C2%2C7%2C+-1%2C10%2C+2%29%29


Step 3. Change the signs of the upper right to lower left
diagonal elements.

%28matrix%282%2C2%2C7%2C+1%2C-10%2C+2%29%29

Step 4. Divide every element by the determinant value
fund in step 1.

%28matrix%282%2C2%2C7%2F24%2C+1%2F24%2C-10%2F24%2C+2%2F24%29%29

Step 5.  Reduce if possible

%28matrix%282%2C2%2C7%2F24%2C+1%2F24%2C-5%2F12%2C+1%2F12%29%29

You do the other two following this same 
5-step rule:

Matrix 2. %28matrix%282%2C2%2C-4%2C+2%2C-5%2C+1%29%29 

answer: %28matrix%282%2C2%2C1%2F6%2C-1%2F3%2C5%2F6%2C-2%2F3%29%29

Matrix 3. %28matrix%282%2C2%2C9%2C+-3%2C-6%2C+2%29%29

answer: Singular matrix, has no inverse.

Edwin