Question Icon

Hotmath Practice Problems

book image
Title:
Hotmath Algebra 2
Author:
Hotmath Team
 
Free
Chapter:Matrices and Matrix OperationsSection:Matrix Multiplication
 
Problem: 1

Can the two matrices given below be multiplied? Why?

Problem: 3

X is a matrix of order 5 2 and Y is a matrix of order 2 4.

Is the matrix product XY defined? Is the matrix product YX defined?

Problem: 5

X is a 7 5 matrix and Y is a 5 4 matrix. Is the matrix product XY defined? What is the order of the product?

Problem: 7

X is a 3 4 matrix and Y is a 4 2 matrix. Is the matrix product XY defined? What is the order of the product?

Problem: 9

X is a 4 1 matrix and Y is a 4 6 matrix. Is the matrix product XY defined? What is the order of the product?

Problem: 11

X is a 9 5 matrix and Y is a 5 7 matrix. Determine if the matrix product XY is defined. What is the order of the product?

Problem: 13

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 15

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 17

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 19

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 21

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 23

Evaluate the given expression:

Problem: 25

Evaluate the given expression:

Problem: 27

Evaluate the given expression:

Problem: 29

Find the value of x and y:

Problem: 31

What is the value of x and y in the given matrix product?

Problem: 33

You have to prepare two bouquets out of roses, carnations and lilies.

The number of each of these flowers is shown in the matrix.

The cost of a rose is $4, cost of a carnation is $2.5 and that of a lily is $5.

If your friend is willing to split the cost of the second bouquet evenly with you, use matrix multiplication to determine how much you'll have to spend.

Problem: 35

The percentage of total world production in the year 1990 of wheat, rice, and corn grown by four countries is given in the matrix below. The total of wheat, rice and corn (in thousands of metric tons) was 525,764, 462,422 and 496,512.Use matrix multiplication to find out how many metric tons of the three grains were grown in each of the four countries.

Problem: 37

What is the order of the given matrix?

Problem: 39

What is the order of the given matrix?

Problem: 41

Determine whether the given statement is true or false. If it is true, determine the order of the matrix. If it is false, give reasons.

"A matrix of order 3 3 can be subtracted from a matrix of order 3 1."

Problem: 43

Determine whether the given statement is true or false. If it is true, determine the order of the matrix. If it is false, give reasons.

"A matrix of order 3 4 can be subtracted from a matrix of order 3 4."

Problem: 45

Determine whether the given statement is true or false. If it is true, determine the order of the matrix. If it is false, give reasons.

"A matrix of order 2 4 can be multiplied by a matrix of order 4 6."

Problem: 47

Illustrate the Left Distributive Property using the information given below:

Left Distributive Property:X(Y +Z) = XY + XZ.

Problem: 49

Illustrate the Property of Scalar Multiplication using the matrices shown below and a = 6:

Property of Scalar Multiplication = a(XY) = (aX)Y = X(aY)

Problem: 1

Can the two matrices given below be multiplied? Why?

Problem: 3

X is a matrix of order 5 2 and Y is a matrix of order 2 4.

Is the matrix product XY defined? Is the matrix product YX defined?

Problem: 5

X is a 7 5 matrix and Y is a 5 4 matrix. Is the matrix product XY defined? What is the order of the product?

Problem: 7

X is a 3 4 matrix and Y is a 4 2 matrix. Is the matrix product XY defined? What is the order of the product?

Problem: 9

X is a 4 1 matrix and Y is a 4 6 matrix. Is the matrix product XY defined? What is the order of the product?

Problem: 11

X is a 9 5 matrix and Y is a 5 7 matrix. Determine if the matrix product XY is defined. What is the order of the product?

Problem: 13

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 15

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 17

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 19

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 21

Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.

Problem: 23

Evaluate the given expression:

Problem: 25

Evaluate the given expression:

Problem: 27

Evaluate the given expression:

Problem: 29

Find the value of x and y:

Problem: 31

What is the value of x and y in the given matrix product?

Problem: 33

You have to prepare two bouquets out of roses, carnations and lilies.

The number of each of these flowers is shown in the matrix.

The cost of a rose is $4, cost of a carnation is $2.5 and that of a lily is $5.

If your friend is willing to split the cost of the second bouquet evenly with you, use matrix multiplication to determine how much you'll have to spend.

Problem: 35

The percentage of total world production in the year 1990 of wheat, rice, and corn grown by four countries is given in the matrix below. The total of wheat, rice and corn (in thousands of metric tons) was 525,764, 462,422 and 496,512.Use matrix multiplication to find out how many metric tons of the three grains were grown in each of the four countries.

Problem: 37

What is the order of the given matrix?

Problem: 39

What is the order of the given matrix?

Problem: 41

Determine whether the given statement is true or false. If it is true, determine the order of the matrix. If it is false, give reasons.

"A matrix of order 3 3 can be subtracted from a matrix of order 3 1."

Problem: 43

Determine whether the given statement is true or false. If it is true, determine the order of the matrix. If it is false, give reasons.

"A matrix of order 3 4 can be subtracted from a matrix of order 3 4."

Problem: 45

Determine whether the given statement is true or false. If it is true, determine the order of the matrix. If it is false, give reasons.

"A matrix of order 2 4 can be multiplied by a matrix of order 4 6."

Problem: 47

Illustrate the Left Distributive Property using the information given below:

Left Distributive Property:X(Y + Z) = XY + XZ.

Problem: 49

Illustrate the Property of Scalar Multiplication using the matrices shown below and a = 6:

Property of Scalar Multiplication = a(XY) = (aX)Y = X(aY)