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Q1. What is the maximum number of different elements needed to write a skew symmetric matrix of order n?

• n²
• n 
• n²-n 
• n²-n+1

Solution

To, write a square matrix of order n, we need n² elements. In a skew symmetric matrix, all the diagonal elements are zeros. So we need only n²-n+1 elements to write a skew symmetric matrix of order n

Q2. If A is a matrix of order 1 × 3 and B is a matrix of order 3 × 4, then the order of the matrix obtained on multiplying A and B is

• 4 × 1
• 3 × 3
• 1 × 4
• 3 × 4

Solution

Q3. The number of elements in a 3 x 2 matrix is not the same as ___

• The number of elements in a 3 x 3 matrix
• The number of elements in a 2 x 3 matrix
• The number of elements in a 6 x 1 matrix
• The number of elements in a 1 x 6 matrix

Solution

The number of elements in a 3 x 2 matrix  is 3 x 2 = 6. In the same way, The number of elements in a 2 x 3 matrix  = 2 x 3 = 6  The number of elements in a 6 x 1 matrix   = 6 x 1 = 6 The number of elements in a 1 x 6 matrix  = 1 x 6 = 6 Whereas, the number of elements in a 3 x 3 matrix is 3 x 3 = 9

Q4. To check whether the matrix B is an inverse of matrix  A, we need to check whether

• AB = I
• BA = I
• AB = BA = I
• Either AB = I,BA = I

Solution

If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse matrix of A and it is denoted by A^{– 1.} In that case A is said to be invertible

Q5. If A is a matrix of order m x n and B is a matrix of order l x p. The product AB of two matrices is defined if,

• n = l
• m = p
• n = p
• m = l

Solution

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B.

Q6. If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A

• Equivalent
•  Inverse
• Adjoint
• none of the above

Solution

A matrix obtained from  a given matrix by an elementary row or column transformation  is the Equivalent of a given matrix  

Q7. If A, B are, respectively m × n, k × l matrices, then both AB and BA are defined if and only if

•   n = k and l = m
•   m = n and k = l
•   m = l and  n = l
•   n = m and k = m

Solution

Order of matrix A is m x n. Order of matrix B is k x l. Now, AB is defined if number of columns of matrix A are equal to number of rows of matrix B. i.e., AB is defined if n = k And, BA is defined if number of columns of matrix B are equal to number of rows of matrix A. i.e., BA is defined if l = m.

Q8. If A is a symmetric matrix, then B' AB is

• Skew symmetric
• Symmetric
• Neither symmetric nor skew symmetric
• Both symmetric and skew symmetric

Solution

 

Q9. Consider the following information regarding the number of men and women workers in three BPOs I, II and III:    Men Women I 35 20 II 20 23 III 25 25         What does the entry in the second row and first column represent if the information is represented as a 3 x 2 matrix?  

• The number of Women in BPO II
• The number of Men in BPO II
• The number of Women in BPO I
• The number of Men in BPO I

Solution

    The second row will represent BPO II and the first column represents, number of men in BPO I , II and III. So, the entry in the second row and first column represents the number of Men in BPO II.

Q10. [5] is a scalar matrix of order

• 2
• 0
• 5
• 1

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