ACT Math : How to multiply a matrix by a scalar

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Matrices

Simplify the following

Possible Answers:

Correct answer:

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 #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:

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 #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:

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 #3 : Matrices

Define matrix .

If , evaluate  .

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

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 #4 : Matrices

Define matrix .

If , evaluate  .

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

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 #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:

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 #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:

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

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

 

Possible Answers:

 

 

Correct answer:

 

Explanation:

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

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