# ACT Math : How to multiply a matrix by a scalar

## Example Questions

### Example Question #1 : Matrices

Simplify the following

Explanation:

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 #3 : Matrices

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

If , then evaluate .

Explanation:

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 #4 : Matrices

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

If , then evaluate .

Explanation:

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 #5 : Matrices

Define matrix .

If , evaluate  .

The correct answer is not among the other responses.

Explanation:

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 #6 : Matrices

Define matrix .

If , evaluate  .

The correct answer is not among the other responses.

Explanation:

Scalar multplication of a matrix is done elementwise, so

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

### Example Question #7 : Matrices

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

If , evaluate .

The correct answer is not given among the other responses.

Explanation:

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 #11 : Matrices

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

If , evaluate .

The correct answer is not given among the other responses.

Explanation:

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