Matrices Self Study Quiz
(115).jpg "Matrices Self Study Quiz - Quiz")
Quiz on the Self Study topic of Matrices done by Ong Tiet Ho, Hwa Chong Institution, 3S422 as Part III of the June Self Study Modules. Topics tested include the basics of matrices, addition, subtraction and multiplication of matrices.
- 1.
Which of the following is impossible?
- A.
Scalar Multiplication
- B.
Matrix Multiplication
- C.
Scalar Division
- D.
Matrix Division
Correct Answer
D. Matrix DivisionExplanation
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.Rate this question:
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- 2.
What is an identity matrix and why is it called an identity matrix?
- A.
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 give a null matrix as a result when multiplied by other matrix.
- B.
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.
- C.
An identity matrix is a matrix with all its entries as 0. It is called an identity matrix as it would give a null matrix as a result when multiplied by any other matrix.
- D.
An identity matrix is a matrix with all its entries as 0. It is called an identity matrix as it would not change the original matrix when multiplied by it.
Correct Answer
B. 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.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.Rate this question:
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- 3.
(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.
A + B
- B.
A - B
- C.
A x B
- D.
A / B
Correct Answer
C. A x BExplanation
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.Rate this question:
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- 4.
Which of the following matrix operations is commutative?
- A.
Addition of Matrices
- B.
Subtraction of Matrices
- C.
Multiplication of Matrices
- D.
Division of Matrices
Correct Answer
A. Addition of MatricesExplanation
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.Rate this question:
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- 5.
Which of the following is not a square matrix?
- A.
(1)
- B.
(5 8) (9 2)
- C.
(4 9) (16 25) (36 49)
- D.
(2 8 7 6 9) (8 7 6 0 3) (7 6 8 3 4) (1 4 7 2 6) (7 8 2 3 0)
Correct Answer
C. (4 9) (16 25) (36 49)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.Rate this question:
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- 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 x2,3 and x1,4 represent? Give your answer in the form x2,3, x1,4.
Correct Answer
6, 7Explanation
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.Rate this question:
- 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.
Correct Answer
order, columns, rows, rows, columnsExplanation
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.Rate this question:
- 8.
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.
Correct Answer
(3 6 24), ImpossibleExplanation
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.Rate this question:
- 9.
A = (4 9 8 2 1) (2) (9) B = (2) (3) (4)Evaluate AB and BA and present your answers as AB, BA.
Correct Answer
(115), Impossible
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