Math Problem Solver

Some of the engineering problems require to compute the iterated value of an operator T. By doing this problem you will learn how the diagonalization method you studied in Linear Algebra helps you to compute this iteration very easily.

Consider the upper triangular matrix 𝑈=[410−462−230000580−5]

Define the linear operator T: R4 → R4 by 𝑇𝑋=𝑈𝑋, where 𝑋=[𝑥1𝑥2𝑥3𝑥4].

(a)

Find all the eigen values of 𝑈.

(b)

Find all the eigen vectors of 𝑈.

(c)

Using (a) and (b) write 𝑈=𝑃𝐷𝑃−1, where D is a diagonal matrix.

(d)

Using (c) Find 𝑇8𝑋 𝑎𝑛𝑑 𝑇9𝑋.