Consider the matrix P = [1, 0, 0; 4, 1, 0; 16, 4, 1] and the identity matrix I of size 3. If a matrix Q = [q_(ij)] satisfies P⁵⁰ - Q = I, what is the value of (q₃₁ + q₃₂)/(q₂₁) ?

Question

Accepted Answer

103. The matrix Q is derived from the relationship P⁵⁰ - Q = I. Using the structure of P and its powers, the elements q₃₁, q₃₂, and q₂₁ are calculated, yielding the ratio (q₃₁ + q₃₂)/q₂₁ = 103.

Consider the matrix P = [1, 0, 0; 4, 1, 0; 16, 4, 1] and the identity matrix I of size 3. If a matrix Q = [q_(ij)] satisfies P⁵⁰ - Q = I, what is the value of (q₃₁ + q₃₂)/(q₂₁) ?

Solution

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