If $A=\begin{bmatrix}1&1\\0&1\end{bmatrix}$, then the value of $A^{20}$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\begin{bmatrix}1&20\\0&1\end{bmatrix}$
Given:
$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$
Matrix $A$ is an upper triangular matrix with eigenvalues 1 and 1.
Use the formula for powers of such matrix:
$A^n = \begin{bmatrix} 1 & n \\ 0 & 1 \end{bmatrix}$
Therefore:
$A^{20} = \begin{bmatrix} 1 & 20 \\ 0 & 1 \end{bmatrix}$