Discrete Mathematics Multiple Choice Questions on “Types of Matrices”.
1. If a matrix A = [A11 A12 ⋯ A1n A21 A2n ⋮ ⋮ An1 An2 ⋯ Ann], order(nxn) Aii = 1, Aij = 0 for i ≠ j. Then that matrix is known as ________
a) Identity matrix
b) Null matrix
c) Singular matrix
d) None of the mentioned
Answer: a
Clarification: 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 = AT
d) A = -AT
Answer: c
Clarification: 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 = AT
d) A = -AT
Answer: d
Clarification: 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
d) None of the mentioned
Answer: a
Clarification: 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
d) None of the mentioned
Answer: b
Clarification: 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
Answer: b
Clarification: Trace is the sum of the elements of leading diagonal of matrix.
7. A square matrix A = [aij ]nxn, if aij = 0 for i > j then that matrix is known as _______
a) Upper triangular matrix
b) Lower triangular matrix
c) Unit matrix
d) Null matrix
Answer: a
Clarification: In upper triangular matrix A = [ aij ]nxn, if aij = 0 for i > j.
8. A square matrix A = [aij ]nxn, if aij = 0 for i < j then that matrix is known as _______
a) Upper triangular matrix
b) Lower triangular matrix
c) Unit matrix
d) Null matrix
Answer: b
Clarification: In lower triangular matrix A = [aij ]nxn, if aij = 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
Answer: c
Clarification: Order of two matrices must be same.
10. For matrix A if AAT = I, I is identity matrix then A is?
a) Orthagonal matrix
b) Nilpotent matrix
c) Idempotent matrix
d) None of the mentioned
Answer: a
Clarification: For orthagonal matrices AAT = I = AT A.