If P = 1 0 1 2 1 , then P 50 is:

P = 1 0 1 2 1 P 2 = 1 0 1 2 1 1 0 1 2 1 = 1 0 1 1 P 3 = 1 0 1 1 1 0 1 2 1 = 1 0 3 2 1 P 4 = 1 0 1 2 1 1 0 3 2 1 = 1 0 2 1 ⋮ ∴ P 50 = 1 0 1 2 + 49 1 2 1 = 1 0 25 1

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Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesProduct of MatricesMedium2 minPYQ_2021

MathematicsMediumsingle choice

If $P = [\begin{array}{l} 1 & 0 \\ \frac{1}{2} & 1 \end{array}],$ then $P^{50}$ is:

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Answer:

Solution:

$P = [\begin{array}{l} 1 & 0 \\ \frac{1}{2} & 1 \end{array}]$

$P^{2} = [\begin{matrix} 1 & 0 \\ \frac{1}{2} & 1 \end{matrix}] [\begin{array}{l} 1 & 0 \\ \frac{1}{2} & 1 \end{array}] = [\begin{array}{l} 1 & 0 \\ 1 & 1 \end{array}]$

$P^{3} = [\begin{array}{l} 1 & 0 \\ 1 & 1 \end{array}] [\begin{matrix} 1 & 0 \\ \frac{1}{2} & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ \frac{3}{2} & 1 \end{matrix}]$

$P^{4} = [\begin{array}{l} 1 & 0 \\ \frac{1}{2} & 1 \end{array}] [\begin{array}{l} 1 & 0 \\ \frac{3}{2} & 1 \end{array}] = [\begin{array}{l} 1 & 0 \\ 2 & 1 \end{array}]$

$⋮$

$∴ P^{50} = [\begin{matrix} 1 & 0 \\ \frac{1}{2} + 49 (\frac{1}{2}) & 1 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 25 & 1 \end{matrix}]$

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Product of Matrices

⏱ 2mℹ️ Source: PYQ_2021

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