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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- September 12th 2009, 01:34 PMhayter221Linear 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.

- September 12th 2009, 08:13 PMHallsofIvy
- September 13th 2009, 07:03 AMhayter221
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?