TS EAMCET · Maths · Matrices
If \(I\) is the identity matrix of order 2 and \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), then for \(n \geq 1\), mathematical induction gives
- A \(A^n=n A-(n-1) I\)
- B \(A^n=n A+(n-1) I\)
- C \(A^n=2^n A-(n+1) I\)
- D \(A^n=2^{n-1} A-(n-1) I\)
Answer & Solution
Correct Answer
(A) \(A^n=n A-(n-1) I\)
Step-by-step Solution
Detailed explanation
Given \(\quad A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\) Now, \(\quad A^2=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\)…
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