Exercise 1.5 - Chapter 1 - Matrices and Determinants - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 1.5

Text Book Back Questions and Answers

Choose the Correct Answer.

Question 1.
The value of x if 

(a) 0, -1
(b) 0, 1
(c) -1, 1
(d) -1, -1
Answer:
(b) 0, 1
Hint:
0 – 1[x² – x] + 0 = 0
⇒ x² – x = 0
⇒ x(x – 1) = 0
⇒ x = 0 (or) x = 1

Question 2.
The value of 

(a) xyz
(b) x + y + z
(c) 2x + 2y + 2z
(d) 0
Answer:
(d) 0
Hint:

= 0 (C₁ and C₂ are proportional)

Question 3.
The cofactor of -7 in the determinant

(a) -18
(b) 18
(c) -7
(d) 7
Answer:
(b) 18
Hint:
A cofactor of -7 = 

= 0 + 18
= 18

Question 4.

(a) Δ
(b) -Δ
(c) 3Δ
(d) -3Δ
Answer:
(b) -Δ
Hint:

Question 5.
The value of the determinant 

(a) abc
(b) 0
(c) a²b²c²
(d) -abc
Answer:
(c) a²b²c²
Hint:

Question 6.
If A is square matrix of order 3 then |kA| is:
(a) k|A|
(b) -k|A|
(c) k³|A|
(d) -k³|A|
Answer:
(c) k³|A|

Question 7.
adj (AB) is equal to:
(a) adj A adj B
(b) adj A^T adj B^T
(c) adj B adj A
(d) adj B^T adj A^T
Answer:
(c) adj B adj A

Question 8.
The inverse matrix of

Question 9.
If A =   such that ad – bc ≠ 0 then A^-1 is:

Hint:

Question 10.
The number of Hawkins-Simon conditions for the viability of input-output analysis is:
(a) 1
(b) 3
(c) 4
(d) 2
Answer:
(d) 2

Question 11.
The inventor of input-output analysis is:
(a) Sir Francis Galton
(b) Fisher
(c) Prof. Wassily W. Leontief
(d) Arthur Cayley
Answer:
(c) Prof. Wassily W. Leontief

Question 12.
Which of the following matrix has no inverse?

Question 13.
Inverse of 

Answer:

Question 14.

Question 15.
If A and B non-singular matrix then, which of the following is incorrect?
(a) A² = I implies A^-1 = A
(b) I^-1 = I
(c) If AX = B then X = B^-1A
(d) If A is square matrix of order 3 then |adj A| = |A|²
Answer:
(c) If AX = B then X = B^-1A
Hint:
If AX = B then X = A^-1B so, X = B^-1A is incorrect.

Question 16.
The value of

(a) 5
(b) 4
(c) 0
(d) -3
Answer:
(c) 0
Hint:

[Take out 4 from R₂ and -3 from R₃]
= 0 (∵ R₂ ≡ R₃)

Question 17.
If A is an invertible matrix of order 2 then det (A^-1) be equal
(a) det (A)

(c) 1
(d) 0
Answer:

Question 18.
If A is 3 × 3 matrix and |A| = 4 then |A^-1| is equal to:

Question 19.
If A is a square matrix of order 3 and |A| = 3 then |adj A| is equal to:
(a) 81
(b) 27
(c) 3
(d) 9
Answer:
(d) 9
Hint:
|adj A| = |A|² = 3² = 9

Question 20.
The value of 

(a) 1
(b) 0
(c) -1
(d) -xyz
Answer:
(b) 0
Hint:

Question 21.
If A =

 , then |2A| is equal to:

(a) 4 cos 2θ
(b) 4
(c) 2
(d) 1
Answer:
(b) 4
Hint:
|2A| = 2² |A|

= 4 [cos²θ + sin²θ]
= 4 × 1
= 4

Question 22.

If Δ = 
  and A_ij is cofactor of a_ij, then value of Δ is given by:

(a) a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃
(b) a₁₁A₁₁ + a₁₂A₂₁ + a₁₃A₃₁
(c) a₂₁A₁₁ + a₂₂A₁₂ + a₂₃A₁₃
(d) a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁
Answer:
(d) a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁

Question 23.
If   then the value of x is:

Answer:

Question 24.

(a) -5
(b) -125
(c) -25
(4) 0
Answer:
(b) -125
Hint:

Question 25.
If any three rows or columns of a determinant are identical then the value of the determinant is:
(a) 0
(b) 2
(c) 1
(d) 3
Answer:
(a) 0