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Math Help - Linear Independence

  1. #1
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    Linear Independence

    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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  2. #2
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    Quote Originally Posted by hayter221 View Post
    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?

    If so, what can you say about the determinant of such a matrix?
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  3. #3
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    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?
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