Question

Are the matrices\[\left[\begin{matrix}-1 & 2 \\ 0 & -1\end{matrix}\right],\left[\begin{matrix}-1 & 5 \\ 0 & -1\end{matrix}\right]\]similar?

Answer 1

I guess they're not similar?!
And i dont think we use terms such as 'similar' for matrices or do we?!

Answer 2

haha apparently there is? that's why i am not sure how to go about doing this question.

Answer 3

Two matrices A and B are similar is there is another matrix M such that
\[A = M^{-1}BM\]

There are lots of ways to think about M, but one them is as the cumulative product of matrices equivalent to Gaussian row reduction.

So two matrices are also similar is one can be row reduced into the other (and hence also vice versa).

Hence one way to ask the question here is this: can you row reduce one of these into the other?

Answer 4

Exactly.