SOLUTION: Find the inverse of each matrix, if it exists... 1.. [-2 -1] [10 7] 2..[-4 2] [-5 1] 3.. [9 -3] [-6 2] 4.. [3 4] [6] [2 3] x=[5] 5..

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the inverse of each matrix, if it exists... 1.. [-2 -1] [10 7] 2..[-4 2] [-5 1] 3.. [9 -3] [-6 2] 4.. [3 4] [6] [2 3] x=[5] 5..      Log On


   

Question 174388: Find the inverse of each matrix, if it exists...

1.. [-2 -1]
[10 7]

2..[-4 2]
[-5 1]

3.. [9 -3]
[-6 2]

4.. [3 4] [6]
[2 3] x=[5]

5..[1 -6 0] [1]
[0 1 -7]x=[4]
[3 0 2] [11]
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
 
%28matrix%282%2C2%2C-2%2C-1%2C10%2C7%29%29
:
take terms a%5B11%5Dand a%5B22%5D and switch their positions. This is simply switching the elements on the main diagonal 
 
take terms a%5B12%5Dand a%5B21%5D and change those numbers to their opposites keeping there positions.

%28matrix%282%2C2%2C7%2C1%2C-10%2C-2%29%29
:now we find the determinant of this matrix
:
product of the main diagonal-product of the other diagonal
:
-14-%28-10%29=-4
:
we take that result and divide every element in the matrix and the result is our inverse matrix
:
%28matrix%282%2C2%2C-7%2F4%2C-1%2F4%2C5%2F2%2C1%2F2%29%29
the way you can check is to multiply the two together and see if your result is the identity matrix....if it is you can rest easy you have the correct answer.
:

:
:
:
2)and 3)
:
now I will let you do the steps to 2 and 3
:
answers to 2 is %28matrix%282%2C2%2C1%2F6%2C-1%2F3%2C5%2F6%2C-2%2F3%29%29
...........3 is no solution as the determinant = 0
:
4)%28matrix%282%2C2%2C3%2C4%2C2%2C3%29%29X or%28matrix%282%2C1%2Ca%2Cb%29%29=%28matrix%282%2C1%2C6%2C5%29%29%29
3a+4b=6
2a+3b=5
:
%28matrix%282%2C3%2C3%2C4%2C6%2C2%2C3%2C5%29%293R2-2R1(Row 2)---->%28matrix%282%2C3%2C3%2C4%2C6%2C0%2C1%2C3%29%29R1-4R2(row 1)---->%28matrix%282%2C3%2C3%2C0%2C-6%2C0%2C1%2C3%29%291/3R1--->%28matrix%282%2C3%2C1%2C0%2C-2%2C0%2C1%2C3%29%29 so we end with 
a=-2
b=3
so X=%28matrix%282%2C1%2C-2%2C3%29%29
:
5) is done the same as 4 but this time you have 3 variables....have fun