Review Exercise Solution
- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Here are multiple-choice questions (MCQs) about matrices:
1- What is the dimension of a 3×4 matrix?
(a) 3
(b) 4
(c) 7
(d) 12
Answer: (a) 3
2- Which of the following matrices is a square matrix?
(a) [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
(b) [[2, 5], [1, 3]]
(c) [[1, 0], [0, 1], [1, 1]]
(d) [[3, 2], [6, 4]]
Answer: (b) [[2, 5], [1, 3]]
3- If A and B are two matrices, then A + B is possible only if:
(a) A and B have the same number of rows and columns.
(b) A and B have the same number of rows.
(c) A and B have the same number of columns.
(d) A and B have different dimensions.
Answer: (a) A and B have the same number of rows and columns.
4- What is the result of the multiplication of two matrices with dimensions 2×3 and 3×4?
(a) 2×4 matrix
(b) 3×4 matrix
(c) 2×3 matrix
(d) 3×3 matrix
Answer: (b) 3×4 matrix
5- The identity matrix of order n has _ on the main diagonal and _ elsewhere.
(a) 1, 1
(b) 0, 1
(c) 1, 0
(d) n, n
Answer: (a) 1, 1
6- The determinant of a 2×2 matrix [[a, b], [c, d]] is given by:
(a) ad – bc
(b) ac – bd
(c) ab – cd
(d) bc – ad
Answer: (a) ad – bc
7- If the determinant of a matrix is zero, then the matrix is:
(a) Square
(b) Singular
(c) Identity
(d) Symmetric
Answer: (b) Singular
8 The product of a matrix and its inverse is always equal to:
(a) Zero matrix
(b) Identity matrix
(c) Square matrix
(d) Diagonal matrix
Answer: (b) Identity matrix
9- If A and B are two matrices, then the transpose of (A + B) is equal to:
(a) A^T + B^T
(b) A + B
(c) A – B
(d) A^T – B^T
Answer: (a) A^T + B^T
10- If A is a square matrix, and A^2 = I, then A is called a/an:
(a) Diagonal matrix
(b) Identity matrix
(c) Inverse matrix
(d) Singular matrix
Answer: (c) Inverse matrix
11- The sum of the elements of the main diagonal of a square matrix is called:
(a) Determinant
(b) Trace
(c) Inverse
(d) Adjacent
Answer: (b) Trace
12- Which operation is NOT allowed for matrices?
(a) Addition
(b) Subtraction
(c) Division
(d) Multiplication
Answer: (c) Division
13- If A and B are two matrices of the same size, then A * B is:
(a) Commutative
(b) Associative
(c) Distributive
(d) None of the above
Answer: (b) Associative
14- If a matrix is symmetric, then its transpose is equal to:
(a) Zero matrix
(b) Identity matrix
(c) Diagonal matrix
(d) The original matrix
Answer: (d) The original matrix
15- The inverse of a matrix A is denoted as:
(a) A^(-1)
(b) A^T
(c) A^2
(d) A^+
Answer: (a) A^(-1)
16- If a matrix has only one row, it is called a:
(a) Diagonal matrix
(b) Row matrix
(c) Column matrix
(d) Square matrix
Answer: (b) Row matrix
17- f the determinant of a square matrix is negative, then the matrix is:
(a) Singular
(b) Invertible
(c) Diagonal
(d) Symmetric
Answer: (b) Invertible
18- The inverse of the identity matrix is equal to:
(a) Identity matrix
(b) Zero matrix
(c) Square matrix
(d) None of the above
Answer: (a) Identity matrix
19- The transpose of a row matrix results in a:
(a) Square matrix
(b) Identity matrix
(c) Row matrix
(d) Column matrix
Answer: (d) Column matrix
20- If A is a 3×3 matrix, and |A| = 0, then A is:
(a) Invertible
(b) Singular
(c) Symmetric
(d) Diagonal
Answer: (b) Singular