Let P= 1 0 0 4 1 0 16 4 1 and I be the identity matrix of order 3. If Q=q_ij is a matrix such that P^50-Q=I, then the value of (q_31+q_32)/q_21 is…

Question

Let P= 1 0 0 4 1 0 16 4 1 and I be the identity matrix of order 3. If Q=q_ij is a matrix such that P^50-Q=I, then the value of (q_31+q_32)/q_21 is equal to

MARKS Content Team · Accepted Answer

Correct answer: (B) 103. P= 1 0 0 4 1 0 16 4 1 ⇒P^2= 1 0 0 8 1 0 16+32 8 1 So, P^3= 1 0 0 12 1 0 16+32+48 12 1 Using symmetry, we can write P^50= 1 0 0 200 1 0 16.50.51/2 200 1 As, P^50 −Q=I⇒Q=P^50 −I=[ 0 0 0 200 0 0 16.50.51/2 200 0 ] , q_31=16.50.51/2, q_32=200 and q_21=200 ∴ (q_31+q_32)/q_21=16.50.51/2.200+1=102+1=103

Let $P = [\begin{matrix} 1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1 \end{matrix}]$ and $I$ be the identity matrix of order $3$ . If $Q = [q_{i j}]$ is a matrix such that $P^{50} - Q = I,$ then the value of $\frac{q_{31} + q_{32}}{q_{21}}$ is equal to

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Let P=1004101641 and I be the identity matrix of order 3. If Q=qij is a matrix such that P50-Q=I, then the value of q31+q32q21 is equal to

Solution

More Matrices Questions

Let $P = [\begin{matrix} 1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1 \end{matrix}]$ and $I$ be the identity matrix of order $3$ . If $Q = [q_{i j}]$ is a matrix such that $P^{50} - Q = I,$ then the value of $\frac{q_{31} + q_{32}}{q_{21}}$ is equal to