MCQs of Matrices

Showing 61 to 69 out of 69 Questions

61.

If A 3x3 matrix and A=2B, then

|A|

=_____

62.

If A=

[\begin{matrix} a & 2 \\ 2 & a \end{matrix}]

and

|A^{3}|

=125, then a=_____

63.

If A=

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

and 3A-

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

, then x=_____

64.

If A=

[\begin{matrix} \sin (x) & \cos (x) \\ \cos (x) & - \sin (x) \end{matrix}]

and A(adj A)=kI then k=_____

65.

If A=

[\begin{matrix} p & q \\ r & s \end{matrix}]

, then

A^{T}

+(adj A)=_____

(a)	$[\begin{matrix} p + s & 0 \\ 0 & p + s \end{matrix}]$
(b)	$[\begin{matrix} p + s & q - r \\ r - q & p + s \end{matrix}]$
(c)	$[\begin{matrix} p - s & r - q \\ q - r & p - s \end{matrix}]$
(d)	$[\begin{matrix} p + s & r - q \\ q - r & p + s \end{matrix}]$

66.

If A=

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

, B=

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

and AB=I, then x=_____

67.

If A=

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

, B=

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

, then

A^{2} + A B + 2 B

=_____

68.

If A=

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

, then

A^{3} - 2 A^{2} - 7 A

=_____

Showing 61 to 69 out of 69 Questions