# Complex numbers + linear algebra = :S

## Homework Statement

Find all complex numbers Z (if any) such that the matrix: (it is 2 by 2)

(2)(-1)
(4)(2)

multiplied by a vector V = ZV has a nonzero solution V.

part b)

for each Z that you found, find all vectors V such that (the same matrix)*V=ZV.

## The Attempt at a Solution

I'm not sure that I even know what this question is asking... could anyone clarify this a little?

And please don't mistake my lack of effort for laziness, I genuinely don't understand the question.

Hurkyl
Staff Emeritus
Gold Member
The question is "solve Av=zv".

(A is the matrix you were given)
(v and z are the indeterminate variables you're solving for)
(v is a vector variable)
(z is a complex variable)

Dick
Homework Helper
In other words, as Hurkyl clarified, it's asking you for eigenvalues and eigenvectors of your matrix. Search on those keywords if you need examples.

So I'm looking for complex numbers such that, when multiplied by a vector, it gives the same results as the matrix multiplied by the same vector?

Dick
Homework Helper
So I'm looking for complex numbers such that, when multiplied by a vector, it gives the same results as the matrix multiplied by the same vector?

Yes, the number times the vector should be the same as the matrix times the vector.

I googled eigenvectors/values but I don't see the relevance to this question :s

How would I find a set of complex numbers that multiplies the same way as a matrix of real numbers? Any hints please?

Last edited:
Dick