Linear AlgebraMatrix Representation Problem

[kr0z3n]

Homework Statement

I'm practicing for my finals this coming week and I'm confused about these 2 problems.

Homework Equations

The Attempt at a Solution

For e). I followed my notes and came up with D=U^-1AU..since its asking for some basis to standard basis. And once computed, its the diagonal matrix.

D=
[-2 0 0]
[0 3 0]
[0 0 1]
So am I doing it right?

For part F). I don't know if its exactly the same method as above or do I need to get S=U^-1V then B=SAS^-1

I'm confused with all this!

 

[HallsofIvy]

You've cut off the critical information: what "L" is!

In general, you write a linear transformation, from vector space, V, to itself, as a matrix, in terms of an ordered basis, by applying that linear transformation to each basis vector in turn, writing the result as a linear combination of those basis vectors. The coefficients of each linear combination give a column of the matrix.