Matrices Self Study Quiz

1.       (9 0 1 3 4)           (0 7 3 0)
A = (5 7 8 2 4)           (1 3 6 2)
      (3 4 2 7 0)     B = (7 8 9 2)
                                    (7 4 3 8)
                                    (8 3 2 5)

Which of the following is possible?

A + B

A - B

A x B

A / B

The given question asks which operation is possible between matrices A and B. In this case, the operation that is possible is the multiplication of matrices A and B. Matrix multiplication is possible when the number of columns in the first matrix (A) is equal to the number of rows in the second matrix (B). In this case, A has 5 columns and B has 5 rows, satisfying the condition for matrix multiplication. Therefore, the correct answer is A x B.

Explanation

The given question asks which operation is possible between matrices A and B. In this case, the operation that is possible is the multiplication of matrices A and B. Matrix multiplication is possible when the number of columns in the first matrix (A) is equal to the number of rows in the second matrix (B). In this case, A has 5 columns and B has 5 rows, satisfying the condition for matrix multiplication. Therefore, the correct answer is A x B.

2. Which of the following is not a square matrix?

(1)

(5 8)(9 2)

(4 9)(16 25)(36 49)

The given answer is not a square matrix because it has 3 rows and 2 columns, which means it does not have an equal number of rows and columns. A square matrix is defined as a matrix where the number of rows is equal to the number of columns.

Explanation

The given answer is not a square matrix because it has 3 rows and 2 columns, which means it does not have an equal number of rows and columns. A square matrix is defined as a matrix where the number of rows is equal to the number of columns.

3. Which of the following is impossible?

Scalar Multiplication

Matrix Multiplication

Scalar Division

Matrix Division

Matrix division is not a defined operation in linear algebra. While scalar multiplication, matrix multiplication, and scalar division are all valid operations, matrix division is not. In order to divide matrices, we can multiply the first matrix by the inverse of the second matrix. However, not all matrices have inverses, so matrix division is not always possible.

Explanation

Matrix division is not a defined operation in linear algebra. While scalar multiplication, matrix multiplication, and scalar division are all valid operations, matrix division is not. In order to divide matrices, we can multiply the first matrix by the inverse of the second matrix. However, not all matrices have inverses, so matrix division is not always possible.

4. Which of the following matrix operations is commutative?

Addition of Matrices

Subtraction of Matrices

Multiplication of Matrices

Division of Matrices

The addition of matrices is commutative because the order in which the matrices are added does not affect the result. This means that if we have two matrices A and B, A + B will give the same result as B + A. In other words, the addition operation is independent of the order of the matrices, making it commutative.

Explanation

The addition of matrices is commutative because the order in which the matrices are added does not affect the result. This means that if we have two matrices A and B, A + B will give the same result as B + A. In other words, the addition operation is independent of the order of the matrices, making it commutative.

5. What is an identity matrix and why is it called an identity matrix?

An identity matrix is a matrix with all diagonal entries as 1 and all non-diagonal entries as 0. It is called an identity matrix as it would not change the original matrix when multiplied by it. This is because multiplying any matrix by the identity matrix is equivalent to multiplying it by 1, which does not change the matrix.

Explanation

An identity matrix is a matrix with all diagonal entries as 1 and all non-diagonal entries as 0. It is called an identity matrix as it would not change the original matrix when multiplied by it. This is because multiplying any matrix by the identity matrix is equivalent to multiplying it by 1, which does not change the matrix.

6.       (8 3 1 2)            (7 8 2   5)
A = (9 3 4 8)     B = (4 8 2 11)     X = A + B
      (5 6 7 0)            (3 7 1   9)

What do x_2,3 and x_1,4 represent? Give your answer in the form x_2,3, x_1,4.

x2,3 represents the value at the 2nd row and 3rd column of matrix X, while x1,4 represents the value at the 1st row and 4th column of matrix X.

Explanation

x2,3 represents the value at the 2nd row and 3rd column of matrix X, while x1,4 represents the value at the 1st row and 4th column of matrix X.

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7. For addition to be possible, two matrices must have the same __________. For multiplication to be possible, the number of __________ in the first matrix must be the same as the number of __________ in the second matrix. The resultant matrix would have the number of __________ the first matrix has, and the number of ___________ the second matrix has.

Fill in the above blanks, with a comma and a space in between succeding answers.

For addition to be possible, two matrices must have the same order. This means that they must have the same number of rows and columns.

For multiplication to be possible, the number of columns in the first matrix must be the same as the number of rows in the second matrix.

The resultant matrix would have the number of rows the first matrix has, and the number of columns the second matrix has.

Explanation

For addition to be possible, two matrices must have the same order. This means that they must have the same number of rows and columns.

For multiplication to be possible, the number of columns in the first matrix must be the same as the number of rows in the second matrix.

The resultant matrix would have the number of rows the first matrix has, and the number of columns the second matrix has.

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8. A = (4 9 8 2 1)           (2)
                                    (9)
                              B = (2)
                                    (3)
                                    (4)

Evaluate AB and BA and present your answers as AB, BA.

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Explanation

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9. A = 3 (1 2 8) B = (5) (7 4 9)

Evaluate A and B and present your answers as A, B with two spacings between each entry in each matrix.

The given answer is correct. To evaluate matrix A, we multiply each entry in the matrix by the scalar 3. So, 3 times 1 is 3, 3 times 2 is 6, and 3 times 8 is 24. Thus, matrix A is (3 6 24). To evaluate matrix B, we cannot perform scalar multiplication as there is only one entry in the matrix. Therefore, it is impossible to evaluate matrix B. Hence, the answer is (3 6 24), Impossible.

Explanation

The given answer is correct. To evaluate matrix A, we multiply each entry in the matrix by the scalar 3. So, 3 times 1 is 3, 3 times 2 is 6, and 3 times 8 is 24. Thus, matrix A is (3 6 24). To evaluate matrix B, we cannot perform scalar multiplication as there is only one entry in the matrix. Therefore, it is impossible to evaluate matrix B. Hence, the answer is (3 6 24), Impossible.

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