This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Types of Matrices”.

1. If a matrix A = [A_{11} A_{12} ⋯ A_{1n} A_{21} A_{2n} ⋮ ⋮ A_{n1} A_{n2} ⋯ A_{nn} ], order(nxn) A_{ii} = 1, A_{ij} = 0 for i ≠ j. Then that matrix is know as

a) Identity matrix

b) Null matrix

c) Singular matrix

d) None of the mentioned

View Answer

Explanation: In unit matrix all diagonal elements are 1 and all other 0.

2. A symmetric matrix is a one in which

a) All diagonal elements are zero

b) All diagonal elements are 1

c) A = A^{T}

d) A = -A^{T}

View Answer

Explanation: For symmetric matrices, matrix remains same even after transpose.

3. An anti-symmetric matrix is a one in which

a) All diagonal elements are zero

b) All diagonal elements are 1

c) A = A^{T}

d) A = -A^{T}

View Answer

Explanation: Foran anti-symmetric matrix, matrix changes it sign after transpose.

4. A matrix having one row and many columns is known as?

a) Row matrix

b) Column matrix

c) Diagonal matrix

4) None of the mentioned

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Explanation: In row matrix there is only one row.

5. A matrix having many rows and one column is known as?

a) Row matrix

b) Column matrix

c) Diagonal matrix

4) None of the mentioned

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Explanation: In column matrix there is only one column.

6. The trace of the matrix is defined as:

a) Sum of all the elements of the matrix

b) Sum of all the elements of leading diagonal of matrix

c) Sum of all non-zero elements of matrix

d) None of the mentioned

View Answer

Explanation: Trace is the sum of the elements of leading diagonal of matrix.

7. A square matrix A = [a_{ij} ]_{nxn}, if a_{ij} = 0 for i > j then that matrix is known as:

a) Upper triangular matrix

b) Lower triangular matrix

c) Unit matrix

d) Null matrix

View Answer

Explanation: In upper triangular matrix A = [ a

_{ij}]

_{nxn}, if a

_{ij}= 0 for i > j.

8. A square matrix A = [a_{ij} ]_{nxn}, if a_{ij} = 0 for i < j then that matrix is known as:

a) Upper triangular matrix

b) Lower triangular matrix

c) Unit matrix

d) Null matrix

View Answer

Explanation: In lower triangular matrix A = [a

_{ij}]

_{nxn}, if a

_{ij}= 0 for i < j.

9. Two matrix can be added if:

a) rows of both the matrices are same

b) columns of both the matrices are same

c) both rows and columns of both the matrices are same

d) number of rows of first matrix should be equal to number of column of second

View Answer

Explanation: Order of two matrices must be same.

10. For matrix A if AA^{T} = I, I is identity matrix then A is :

a) Orthagonal matrix

b) Nilpotent matrix

c) Idempotent matrix

d) None of the mentioned

View Answer

Explanation: For orthagonal matrices AA

^{T}= I = A

^{T}A.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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