Let A be an m x n matrix, where m<n, then A^t(A) is an n by n matrix. show that det(A^t(A))=0

also if A is a 2 x 3 matrix can you say that det (AA^t)=0

thanks

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- Apr 24th 2009, 07:01 PMb0mb3rzmatrix and determinants
Let A be an m x n matrix, where m<n, then A^t(A) is an n by n matrix. show that det(A^t(A))=0

also if A is a 2 x 3 matrix can you say that det (AA^t)=0

thanks - Apr 24th 2009, 07:13 PMJameson
I'm not the best at Linear Algebra but I'll give this a crack until someone else helps you out.

I'm assuming A^t(A) to mean the transpose matrix of A. So if A is an m x n matrix then the transpose should be n x m, since the rows and columns switch.

Before I try to help, is this what you meant? - Apr 24th 2009, 07:18 PMb0mb3rz
yeah it is and it says hint, consider the system of homogeneous linear equations Ax=0

- Apr 24th 2009, 07:33 PMJameson
- Apr 24th 2009, 08:40 PMNonCommAlg