linear algebra 231

Question

A= [ 2 5

4 8 ]

find p(A)

p(A)= x³-2x+4

Answer 1

Hello Noor, thank you for your question!

To solve this one you just want to apply the transformation to each value in the matrix. Meaning that you are plugging in x = 2, x = 5, x = 4, and x = 8 into the function P(x) = x^3 – 2x + 4.

P(2) = 2^3 – 2(2) + 4 = 8

P(5) = 5^3 – 2(5) + 4 = 119

P(4) = 4^3 – 2(4) + 4 = 60

P(8) = 8^3 – 2(8) + 4 = 500

So the new matrix would be [8, 119; 60, 500]