If X = begin{bmatrix} 3 & -4 1 & -1 end{bmat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $X = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}$.We calculate $X^2 = X 	imes X = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix} \begin{

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Given $X = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}$.We calculate $X^2 = X 	imes X = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix} \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix} = \begin{bmatrix} (3)(3) + (-4)(1) & (3)(-4) + (-4)(-1) \ (1)(3) + (-1)(1) & (1)(-4) + (-1)(-1) \end{bmatrix} = \begin{bmatrix} 9-4 & -12+4 \ 3-1 & -4+1 \end{bmatrix} = \begin{bmatrix} 5 & -8 \ 2 & -3 \end{bmatrix}$.Now,let us check the options for $n=2$:Option $(a)$ gives $\begin{bmatrix} 3(2) & -4(2) \ 2 & -2 \end{bmatrix} = \begin{bmatrix} 6 & -8 \ 2 & -2 \end{bmatrix} 
eq X^2$.Option $(b)$ gives $\begin{bmatrix} 2+2 & 5-2 \ 2 & -2 \end{bmatrix} = \begin{bmatrix} 4 & 3 \ 2 & -2 \end{bmatrix} 
eq X^2$.Option $(c)$ gives $\begin{bmatrix} 3^2 & (-4)^2 \ 1^2 & (-1)^2 \end{bmatrix} = \begin{bmatrix} 9 & 16 \ 1 & 1 \end{bmatrix} 
eq X^2$.Since none of the options match $X^2$,the correct answer is $(d)$.

If $X = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$,then the value of $X^n$ is

Similar Questions

If matrix $A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $A^{16} = $

If $A$ is a nilpotent matrix of index $2$,then $A(I_2+A)^{51}$ is equal to (where $I_2$ is the identity matrix of order $2$)

If $A$ and $B$ are skew-symmetric matrices of the same order,then $AB - BA$ is a . . . . . . .

Express the following matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{ccc}3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2\end{array}\right]$

Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$,where $a, b \in \mathbb{N}$. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module