If A={bmatrix}1 & 8\\0 & 1{bmatrix} then A^8=

Correct Answer is : [16401]{bmatrix}1 & 64\\0 & 1{bmatrix}[10641]

{bmatrix}1 & 64\\0 & 1{bmatrix}

{bmatrix}1 & 32\\0 & 1{bmatrix}

{bmatrix}1 & 16\\0 & 1{bmatrix}

If A={bmatrix}1 & 8\\0 & 1{bmatrix} then A^8=

Correct Answer is : [16401]{bmatrix}1 & 64\\0 & 1{bmatrix}[10641]

Test Index

AP ICET 2024 6th May 2024 Shift 1

Question : 175 of 200

Marks: +1, -0

A=\begin{bmatrix}1 & 8\\0 & 1\end{bmatrix}

then

A^8=

$\begin{bmatrix}1 & 64\\0 & 1\end{bmatrix}$
$\begin{bmatrix}1 & 32\\0 & 1\end{bmatrix}$
$\begin{bmatrix}1 & 16\\0 & 1\end{bmatrix}$
$\begin{bmatrix}1 & 8\\0 & 1\end{bmatrix}$

Validate

Solution:

For the matrix

A=\begin{bmatrix}1 & 8\\0 & 1\end{bmatrix}

, notice that this is a special form of a matrix. We can calculate the power of the matrix by recognizing the structure of the matrix and multiplying it repeatedly. When we compute

A^8

, we get:

A^8=\begin{bmatrix}1 & 8\\0 & 1\end{bmatrix}^8=\begin{bmatrix}1 & 8 \times 8\\0 & 1\end{bmatrix}=\begin{bmatrix}1 & 64\\0 & 1\end{bmatrix}

Quick Tip

For matrices of this special form, raising them to a power simply involves multiplying the off-diagonal element by the power of the exponent.

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