### All ACT Math Resources

## Example Questions

### 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 #2 : 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 #3 : 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 #4 : 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

### Example Question #2 : How To Multiply A Matrix By A Scalar

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 second element in the second row, which is 6; similarly, . The equation becomes

### Example Question #3 : How To Multiply A Matrix By A Scalar

**Possible Answers:**

**Correct answer:**

When multiplying a constant to a matrix, multiply each entry in the matrix by the constant.

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