Help, math, matrix, calculus

Question

Hi, I need some help with simple mathematics, matrix

Given the matrix

6 -2 *

B = * 6 -1

-1 * 5

a) Find the missing coefficients in the matrix B so that it becomes orthogonally diagonalizable.

b) Diagonalize the matrix B orthogonally (you can use a calculator or other computer tool to solve the characteristic equation).

c) Use the result in b) to find B ^ n.

Answer 1

a)

For B to be orthogonally diagonalizable, it needs to be symmetric.

That condition provides all the missing entries

6 -2 -1

B = -2 6 -1

-1 -1 5

b)

There are many websites that give you the diagonalization

B = PDP-1

c)

Then you use the relation

Bⁿ = PDⁿP^-1

I am not sure what value of n you have in mind, but it works for any value.