SOLUTION: Find the inverse of each matrix if it exists. If it does not exist, write no inverse. 1. [6 2] [3 2] 2. [1 2 3] [2 2 1] [1 1 1] 3. [7 8] [-14

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find the inverse of each matrix if it exists. If it does not exist, write no inverse. 1. [6 2] [3 2] 2. [1 2 3] [2 2 1] [1 1 1] 3. [7 8] [-14       Log On


   

Question 175886: Find the inverse of each matrix if it exists. If it does not exist, write
no inverse.
1. [6 2]
[3 2]

2. [1 2 3]
[2 2 1]
[1 1 1]



3. [7 8]
[-14 -16]

4. [4 4 8]
[3 2 6]
[2 1 4]


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started

1)

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

To find the inverse of the matrix A=%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29 is abs%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29=6. So this means that d=6

Step 2) Swap the values



Now switch the highlighted values %28matrix%282%2C2%2Chighlight%286%29%2C2%2C3%2Chighlight%282%29%29%29 to get %28matrix%282%2C2%2Chighlight%282%29%2C2%2C3%2Chighlight%286%29%29%29

Step 3) Change the sign



Now change the sign of the highlighted values %28matrix%282%2C2%2C2%2Chighlight%282%29%2Chighlight%283%29%2C6%29%29 to get %28matrix%282%2C2%2C2%2Chighlight%28-2%29%2Chighlight%28-3%29%2C6%29%29

Step 4) Multiply by the inverse of the determinant



Multiply by 1%2Fd to get %281%2Fd%29%28matrix%282%2C2%2C2%2C-2%2C-3%2C6%29%29

Plug in d=6 to get %281%2F6%29%28matrix%282%2C2%2C2%2C-2%2C-3%2C6%29%29

Step 5) Multiply 1%2F6 by every element in the matrix (simplify and reduce if possible)



Multiply 1%2F6 by EVERY element to get

Multiply to get %28matrix%282%2C2%2C2%2F6%2C-2%2F6%2C-3%2F6%2C6%2F6%29%29

Reduce each element: %28matrix%282%2C2%2C1%2F3%2C-1%2F3%2C-1%2F2%2C1%29%29


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Answer:

So the inverse of %28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29 is %28matrix%282%2C2%2C1%2F3%2C-1%2F3%2C-1%2F2%2C1%29%29

This means that if A=%28matrix%282%2C2%2C6%2C2%2C3%2C2%29%29 then A%5E%28-1%29=%28matrix%282%2C2%2C1%2F3%2C-1%2F3%2C-1%2F2%2C1%29%29






2)

In order to find the inverse of %28matrix%283%2C3%2C1%2C2%2C3%2C2%2C2%2C1%2C1%2C1%2C1%29%29, we need to find the row reduced form of


This solution was generated by the Linear Algebra Toolkit


Photobucket



Notice how the right hand matrix is %28matrix%283%2C3%2C-1%2C-1%2C4%2C1%2C2%2C-5%2C0%2C-1%2C2%29%29


So this means that the inverse of %28matrix%283%2C3%2C1%2C2%2C3%2C2%2C2%2C1%2C1%2C1%2C1%29%29 is %28matrix%283%2C3%2C-1%2C-1%2C4%2C1%2C2%2C-5%2C0%2C-1%2C2%29%29