Matrices mcqs

Question 1.
The value of k for which the points (k, 1)., (5, 5) and (10, 7) may be collinear if: 
(a) k = -5
(b) k = 7
(c) k = 9
(d) k = 1
Answer:
Formula
Points (x₁; y₁) ; (x₂; y₂) and (x₃; y₃) are collinear; if
∣∣∣∣x1x2x3y1y2y3111∣∣∣∣ = 0

⇒ ∣∣∣∣K510157111∣∣∣∣ = 0
or; K(5 – 7) – 1(5 – 10) + 1(35 – 50) = 0
or; -2K + 5 – 15 = 0 or K = -5
(a) is correct.

Question 2.
If |A| = 0, then A is: 
(a) 0
(b) Uro matrix
(c) Singular matrix
(d) Non-Singular matrix
Answer:
(c)
If |A| = 0, Then,
Matrix – A is called Singular Matrix.

Question 3.
If A = [2iii−i] if i² = -1 then |A| = ?
(a) 2
(b) 3
(c) 4
(d) 5
Solution:
(b)
|A| = ∣∣∣2iii−i∣∣∣ = -2i² – i²
= -3i² = -3(-1) = 3

Question 4.
If A and B are matrices then which from the following is true ? 
(«) A + B ≠B + A
(b) (A’)² ≠ A
(c) AB ≠ BA
(d) all are true
Answer:
(c)

Question 5.
Transpose of a rectangular matrix is a: 
(a) Rectangular matrix
(b) Diagonal matrix
(c) Square matrix
(d) Scalar matrix
Answer:
(a)

Question 6.
If A = [−512−3], then adj. A is 
(a) [−3−1−2−5]
(b) [3−1−25]
(c) [5213]
(d) [3125]
Answer:
(a)

Question 7.
If A = [5yx0] and A = A^T, then 
(a) x = 0, y = 5
(b) x = y
(c) x + y =5
(d) None
Answer:
(b)
A = A^T
∴ [5yx0]=[5xy0]
⇒ x = y

Question 8.
Let A^T be the transpose of matrix A having order m × n, then (A^T. A) is a matrix of order: 
(a) m × m
(b) n × n
(c) m × n
(d) n × m
Answer:
(a)
Order of A^T is m × n
Order of A = n × m
Order of (A^T_{m × n} . A_{n × m})
= m × m

Question 9.
If (x+y11x−y)+(223−4)=(12340) then 
(a) x = 7, y = -3
(b) x = -7, y = -3
(c) x = -7, y = 3
(d) x = 7, y = 3
Answer:
(d)
TRICKS:
Go by Choices
(d) satisfies it

Question 10.
[1 2 3]⎡⎣⎢log102log103log104⎤⎦⎥ = .
(a) log₁₀(1521)
(b) log₁₀(1152)
(c) log₁₀(5211)
(d) log₁₀(2151)
Answer:
(b)
[1 2 3]⎡⎣⎢log102log103log104⎤⎦⎥
1.log₁₀ 2 + 2log₁₀3 + 3log₁₀4
= log₁₀2 + log₁₀3² +log₁₀ 4³
= l0g₁₀ (2.9.64) = log₁₀1152