Question: True or False, the product of two linear independent matrices is linear independent. (assuming the matrices can be multiplied) Provide a full proof or counter example.
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Question: True or False, the product of two linear independent matrices is linear independent. (assuming the matrices can be multiplied) Provide a full proof or counter example.
What do you mean by "linear independent matrix"? A matrix whose rows (or columns), thought of as vectors, are indendent?Quote:
Originally Posted by hayter221
If so, what can you say about the determinant of such a matrix?
Yes, the problem is referring to the rows/columns being independent. It refers to the matrices as "vector sets" so I assume its actually talking of columns. This would mean their determinants cannot equal zero, but how can this help, would i set up two matrices of this type and show that the det cannot equal zero?