MCQs of Matrices

Matrices MCQs

Showing 71 to 80 out of 92 Questions

71.

If A=

[\begin{matrix} 4 & 2 \\ - 1 & 1 \end{matrix}]

, then (A-2I)(A-3I)=_____

(a)	A
(b)	I
(c)	0
(d)	5I

72.

Suppose that X=

[\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}]

, A=

[\begin{matrix} 1 & - 1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1 \end{matrix}]

and B=

[\begin{matrix} 3 \\ 1 \\ 4 \end{matrix}]

and AX=B, then X=_____

(a)	$[\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$
(b)	$[\begin{matrix} - 1 \\ - 2 \\ 3 \end{matrix}]$
(c)	$[\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}]$
(d)	$[\begin{matrix} - 1 \\ 2 \\ 3 \end{matrix}]$

73.

If 2X+

[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] = [\begin{matrix} 3 & 8 \\ 7 & 2 \end{matrix}]

, then X=_____

(a)	$[\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix}]$
(b)	$[\begin{matrix} 1 & - 3 \\ 2 & - 1 \end{matrix}]$
(c)	$[\begin{matrix} 2 & 6 \\ 4 & - 2 \end{matrix}]$
(d)	$[\begin{matrix} 2 & - 6 \\ 4 & - 2 \end{matrix}]$

74.

if A=

[\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}]

and I=

[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

, then which of the following is true ?

\forall n \in N

(a)	$A^{n} = n A + (n - 1) I$
(b)	$A^{n} = 2^{n - 1} A + (n - 1) I$
(c)	$A^{n} = n A - (n - 1) I$
(d)	$A^{n} = 2^{n - 1} A - (n - 1) I$

75.

ω

is a complex cube root of unity and H=

[\begin{matrix} ω & 0 \\ 0 & ω \end{matrix}]

, then

H^{70}

=_____

(a)	0
(b)	-H
(c)	H
(d)	$H^{2}$

76.

If A=

[\begin{matrix} 5 & 5 α & α \\ 0 & α & 3 α \\ 0 & 0 & 5 \end{matrix}]

and

|A^{2}|

=25, then

|α|

=_____

(a)	1
(b)	$\frac{1}{5}$
(c)	5
(d)	$5^{2}$

77.

If A=

[\begin{matrix} α^{2} & 5 \\ 5 & - α \end{matrix}]

and

|A^{10}|

=1024, then

α

=_____

(a)	2
(b)	-2
(c)	3
(d)	-3

78.

If A=

[\begin{matrix} a & b \\ c & d \end{matrix}]

such that ad-bc

\neq

0, then

A^{- 1}

=_____

(a)	$\frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}]$
(b)	$\frac{1}{a d - b c} [\begin{matrix} d & b \\ - c & a \end{matrix}]$
(c)	$[\begin{matrix} d & - b \\ - c & a \end{matrix}]$
(d)	None of the above

79.

[\begin{matrix} 3 & 2 & 0 \end{matrix}] [\begin{matrix} 1 & 2 & 2 \\ - 2 & - 1 & - 1 \\ 1 & - 4 & - 3 \end{matrix}] [\begin{matrix} 3 \\ 2 \\ 0 \end{matrix}] = [_____]

(a)	5
(b)	$\frac{5}{2}$
(c)	4
(d)	$\frac{3}{2}$

80.

For matrix multiplication_____is true.

(a)	associativity
(b)	commutativity
(c)	Both(a) and (b)
(d)	None of the above

Showing 71 to 80 out of 92 Questions