# GRE Subject Test: Math : Linear Algebra

## Example Questions

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### Example Question #1 : Linear Algebra

Perform the following operation.

Explanation:

The first step to solving this operation is to do the multiplication:

Once we have multiplied the matrices, we can perform the addition portion:

### Example Question #2 : Linear Algebra

Perform the following operation.

Explanation:

The first step is to solve whatever is in the parentheses, in this case it is addition:

We then substitute our solution into the parentheses:

Our next, and final step in this problem, is to carry out the multiplication:

### Example Question #3 : Linear Algebra

Find the inverse of the following matrix, if possible.

The inverse does not exist.

Explanation:

Write the formula to find the inverse of a matrix.

Substituting in the given matrix we are able to find the inverse matrix.

### Example Question #4 : Linear Algebra

Find the inverse of the following matrix, if possible.

The inverse does not exist.

Explanation:

Write the formula to find the inverse of a matrix.

Using the given information we are able to find the inverse matrix.

### Example Question #5 : Linear Algebra

Find the inverse of the function.

Explanation:

To find the inverse function, first replace  with :

Now replace each  with an  and each  with a :

Solve the above equation for :

Replace  with . This is the inverse function:

### Example Question #6 : Linear Algebra

Find the inverse of the function .

Explanation:

To find the inverse of , interchange the  and  terms and solve for .

### Example Question #3 : Find The Inverse Of A Function

Find the inverse of the following equation.

.

Explanation:

To find the inverse in this case, we need to switch our x and y variables and then solve for y.

Therefore,

becomes,

To solve for y we square both sides to get rid of the sqaure root.

We then subtract 2 from both sides and take the exponenetial of each side, leaving us with the final answer.

### Example Question #4 : Find The Inverse Of A Function

Find the inverse of the following function.

Explanation:

To find the inverse of y, or

first switch your variables x and y in the equation.

Second, solve for the variable  in the resulting equation.

Simplifying a number with 0 as the power, the inverse is

### Example Question #5 : Find The Inverse Of A Function

Find the inverse of the following function.

Does not exist

Explanation:

To find the inverse of y, or

first switch your variables x and y in the equation.

Second, solve for the variable  in the resulting equation.

And by setting each side of the equation as powers of base e,

### Example Question #11 : Inverse Functions

Find the inverse of the function.