# Linear Independence

• Sep 12th 2009, 01:34 PM
hayter221
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.
• Sep 12th 2009, 08:13 PM
HallsofIvy
Quote:

Originally Posted by hayter221
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?
• Sep 13th 2009, 07:03 AM
hayter221
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?