### All ACT Math Resources

## Example Questions

### Example Question #1 : Matrices

Evaluate:

**Possible Answers:**

**Correct answer:**

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

### Example Question #1 : Matrices

What is ?

**Possible Answers:**

**Correct answer:**

You can begin by treating this equation just like it was:

That is, you can divide both sides by :

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore,

### Example Question #1 : Matrices

If , what is ?

**Possible Answers:**

**Correct answer:**

Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :

Now, this means that your equation looks like:

This simply means:

and

or

Therefore,

### Example Question #1 : Matrices

Simplify:

**Possible Answers:**

**Correct answer:**

Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.

### Example Question #1 : Matrices

Simplify the following

**Possible Answers:**

**Correct answer:**

When multplying any matrix by a scalar quantity (3 in our case), we simply multiply each term in the matrix by the scalar.

Therefore, every number simply gets multiplied by 3, giving us our answer.

### Example Question #1 : How To Multiply A Matrix By A Scalar

Define matrix , and let be the 3x3 identity matrix.

If , then evaluate .

**Possible Answers:**

**Correct answer:**

The 3x3 identity matrix is

Both scalar multplication of a matrix and matrix addition are performed elementwise, so

is the first element in the third row of , which is 3; similarly, . Therefore,

### Example Question #7 : Matrices

Define matrix , and let be the 3x3 identity matrix.

If , then evaluate .

**Possible Answers:**

**Correct answer:**

The 3x3 identity matrix is

Both scalar multplication of a matrix and matrix addition are performed elementwise, so

is the first element in the third row of , which is 3; similarly, . Therefore,

### Example Question #1 : Matrices

Define matrix .

If , evaluate .

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

If , then .

Scalar multplication of a matrix is done elementwise, so

is the first element in the second row of , which is 5, so

### Example Question #9 : Matrices

Define matrix .

If , evaluate .

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

Scalar multplication of a matrix is done elementwise, so

is the third element in the second row of , which is 1, so

### Example Question #10 : Matrices

Define matrix , and let be the 3x3 identity matrix.

If , evaluate .

**Possible Answers:**

The correct answer is not given among the other responses.

**Correct answer:**

The 3x3 identity matrix is

Both scalar multplication of a matrix and matrix addition are performed elementwise, so

is the first element in the second row, which is 5; similarly, . The equation becomes

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