If P = λ 0 1 1 and Q = 4 0 3 1 such that P 2 = Q , then P 3 is equal to

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

If

P = [\begin{matrix} λ & 0 \\ 1 & 1 \end{matrix}]

and

Q = [\begin{matrix} 4 & 0 \\ 3 & 1 \end{matrix}]

such that

P^{2} = Q,

then

P^{3}

is equal to

MathematicsMatricesJEE Main

Options:

A $[\begin{matrix} 8 & 0 \\ 7 & 1 \end{matrix}]$
B $[\begin{matrix} 10 & 1 \\ 8 & 0 \end{matrix}]$
C $[\begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}]$
D $[\begin{matrix} 6 & 0 \\ 4 & 1 \end{matrix}]$

Solution:

1528 Upvotes Verified Answer

The correct answer is:

[\begin{matrix} 8 & 0 \\ 7 & 1 \end{matrix}]

P^{2} = [\begin{matrix} λ & 0 \\ 1 & 1 \end{matrix}] [\begin{matrix} λ & 0 \\ 1 & 1 \end{matrix}] = [\begin{matrix} λ^{2} & 0 \\ λ + 1 & 1 \end{matrix}] = [\begin{matrix} 4 & 0 \\ 3 & 1 \end{matrix}]

So,

λ = 2

Hence,

P^{3} = [\begin{matrix} 2 & 0 \\ 1 & 1 \end{matrix}] [\begin{matrix} 4 & 0 \\ 3 & 1 \end{matrix}] = [\begin{matrix} 8 & 0 \\ 7 & 1 \end{matrix}]

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play