Matrices
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$, then $A^n$ is:
(a) $\begin{bmatrix} 1 & 0 \\ n & 1 \end{bmatrix}$
(b) $\begin{bmatrix} n & 0 \\ n & n \end{bmatrix}$
(c) $\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$
(d) $\begin{bmatrix} n & 0 \\ 1 & n \end{bmatrix}$
Step-by-Step Solution
By mathematical induction, A^n = [[1, 0], [n, 1]]. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\begin{bmatrix} 1 & 0 \\ n & 1 \end{bmatrix}$: 1.0 Mark
Correct Answer: $\begin{bmatrix} 1 & 0 \\ n & 1 \end{bmatrix}$
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