SOLUTION: 7 2 determine whether the matrix has an inverse. If an inverse exists, find it. 0 -3

Question 365778: 7 2 determine whether the matrix has an inverse. If an inverse exists, find it.
0 -3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
A matrix has an inverse if the determinant is nonzero.

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

If you have the general 2x2 matrix:

the determinant is:

So this means that

Note: the vertical bars denote a determinant.

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So in this case the determinant of is:

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Answer:

So which means that the determinant of the matrix is -21

Since the determinant is nonzero, this means that the inverse exists.

So let's find the inverse...

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

To find the inverse of the matrix , we can follow these steps:

Step 1) Find the determinant

The determinant of is . So this means that

Step 2) Swap the values

Now switch the highlighted values to get

Step 3) Change the sign

Now change the sign of the highlighted values to get

Step 4) Multiply by the inverse of the determinant

Multiply by to get

Plug in to get

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

Multiply by EVERY element to get

Multiply to get

Reduce each element:

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

Answer:

So the inverse of is

This means that if then

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