puhsyers
Jan23-12, 11:24 PM
Hi everyone,
This not a homework question. I'm reviewing some linear algebra and I found this on a worksheet. I just need a hint on how to approach this problem.
Let β=\{ v_1,v_2,...,v_n\} be a basis for R^n . Let M be the matrix whose columns are the basis vectors in β. Do the columns of M^2 form a basis?
I've played around with some examples and it seems to be true. I know that M has full rank and hence invertible, therefore, M^2 is also invertible and has full rank. But this only means the columns of M^2 spans the vector space. How do I show the columns are also linearly independent?
This not a homework question. I'm reviewing some linear algebra and I found this on a worksheet. I just need a hint on how to approach this problem.
Let β=\{ v_1,v_2,...,v_n\} be a basis for R^n . Let M be the matrix whose columns are the basis vectors in β. Do the columns of M^2 form a basis?
I've played around with some examples and it seems to be true. I know that M has full rank and hence invertible, therefore, M^2 is also invertible and has full rank. But this only means the columns of M^2 spans the vector space. How do I show the columns are also linearly independent?