MCQs of Matrices

Showing 11 to 20 out of 92 Questions

11.

I f i n v e r s e o f A = [\begin{matrix} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{matrix}] i s \frac{1}{10} [\begin{matrix} 4 & 2 & 2 \\ - 5 & 0 & α \\ 1 & - 2 & 3 \end{matrix}], t h e n α =_____.

12.

I f A B = B A a n d A = [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}], t h e n B =_____.

13.

I f A = [\begin{matrix} 1 & 3 \\ 3 & 4 \end{matrix}] a n d A^{2} - k A - 5I = 0, t h e n k =_____.

14.

If A = (\begin{matrix} 1 & 3 \\ 3 & 4 \end{matrix}) and A^{2} - kA - 51 = O, then k =_____.

15.

M a t r i x A = [\begin{matrix} 0 & 2 y & z \\ x & y & - z \\ x & - y & z \end{matrix}] i f A A^{T} = I, t h e n (x, y, z) = (_____,_____,_____) . (x, y, z > 0)

16.

I f A [\begin{matrix} 1 & - 2 & - 5 \\ 3 & 4 & 0 \end{matrix}] = [\begin{matrix} - 1 & - 8 & - 10 \\ 1 & - 2 & - 5 \\ 9 & 22 & 15 \end{matrix}], t h e n A =_____.

17.

I f A = [\begin{matrix} \cos \frac{2 π}{3} & - \sin \frac{2 π}{3} \\ \sin \frac{2 π}{3} & \cos \frac{2 π}{3} \end{matrix}], t h e n A^{3} =_____.

18.

C h e c k, w h e t h e r \frac{1}{11} [\begin{matrix} - 1 & 8 & α \\ 1 & - 19 & 14 \\ 2 & 6 & - 5 \end{matrix}] i s a n i n v e r s o f A = [\begin{matrix} 1 & 2 & 5 \\ 3 & 1 & 1 \\ 4 & 2 & 1 \end{matrix}], i f s o, t h e n α =_____.

19.

[\begin{matrix} x & 0 \\ 1 & y \end{matrix}] - [\begin{matrix} 2 & - 4 \\ - 3 & - 4 \end{matrix}] = [\begin{matrix} 3 & 5 \\ 6 & 3 \end{matrix}] - [\begin{matrix} 2 & 1 \\ 2 & 1 \end{matrix}]

, then x = _____, y = _____.

20.

If [1 x 1] [\begin{matrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ x \end{matrix}] = 0, then x =_____.

Showing 11 to 20 out of 92 Questions