Power Matrix

Question

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

• A. $\begin{bmatrix} 3n & -4n \\ n & -n \end{bmatrix}$
• B. $\begin{bmatrix} 2+n & 5-n \\ n & -n \end{bmatrix}$
• C. $\begin{bmatrix} 3^n & (-4)^n \\ 1^n & (-1)^n \end{bmatrix}$
• D. None of the above

Comments

I think answer is D).

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What should be Xⁿ ?

Answer 1

Answer is D).

Given Matrix ,

$X=\begin{bmatrix} 3 &-4 \\ 1 & -1 \end{bmatrix}$.

$X^{2}=\begin{bmatrix} 5 &-8 \\ 2 & -3 \end{bmatrix}$.

$X^{3}=\begin{bmatrix} 7 &-12 \\ 3 & -5 \end{bmatrix}$

Correct solution for above matrix is :

$X^{n}=\begin{bmatrix} 2n+1 &-4n \\ n & 1-2n \end{bmatrix}$

Comments

sry sir, i didnt knew how to make a matrix here... :)

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Can you explain how you reached to that conclusion ?