First slide

Operations of matrix

Question

If $A = [\begin{matrix} 1 & 0 \\ 1 / 2 & 1 \end{matrix}]$ , then A¹⁰⁰ is equal to

Moderate

A

$[\begin{matrix} 1 & 0 \\ 110 & 1 \end{matrix}]$
B

$[\begin{matrix} 1 & 0 \\ 50 & 1 \end{matrix}]$
C

$[\begin{matrix} 1 & 0 \\ 25 & 1 \end{matrix}]$
D

None of these

Solution

$A^{2} = [\begin{matrix} 1 & 0 \\ 1 / 2 & 1 \end{matrix}] [\begin{matrix} 1 & 0 \\ 1 / 2 & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 2 (1 / 2) & 1 \end{matrix}]$
$A^{3} = A^{2} \times A = [\begin{matrix} 1 & 0 \\ 2 (1 / 2) & 1 \end{matrix}] [\begin{matrix} 1 & 0 \\ 1 / 2 & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 3 (1 / 2) & 1 \end{matrix}]$
Continuing in this way, we get
$A^{100} = [\begin{matrix} 1 & 0 \\ 100 (1 / 2) & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 50 & 1 \end{matrix}]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App