- #1

RJLiberator

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## Homework Statement

Prove that if [itex]({A_1, A_2, ..., A_k})[/itex] is a linearly independent subset of M_nxn(F), then [itex](A_1^T,A_2^T,...,A_k^T)[/itex] is also linearly independent.

## Homework Equations

## The Attempt at a Solution

Have: [itex]a_1A_1^T+a_2A_2^T+...+a_kA_k^T=0[/itex] implies [itex]a_1A_1+a_2A_2+...+a_kA_k=0[/itex]

So [itex]a_1=a_2=a_3=a_n...=0[/itex]

^^ This was the answer in the back of the book, but I'm not sure what it means.

I guess I have to assume that the T means transpose here. It's safe to assume that since it's linear independent, then the transpose is also linear independent?