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## Homework Statement

If the rows of A are linearly dependent, prove that the rows of AB are also linearly dependent.

## The Attempt at a Solution

[tex] A = \begin{pmatrix}a&-a\\b&-b\end{pmatrix}[/tex] the rows are linearly dependent because a - a = 0 and b - b = 0.

[tex] B = \begin{pmatrix}c_1&c_2\\c_3&c_4\end{pmatrix}[/tex]

Then[tex] AB = \begin{pmatrix}a(c_1-c_3)&a(c_2-c_4)\\b(c_1-c_3)&b(c_2-c_4)\end{pmatrix} \; where\; c_1 \neq c_3\; and\; c_2 \neq c_4[/tex]

But then wouldn't these rows now be linearly

**independent**? Unless [tex] c_1 - c_3 = -(c_2 - c_4)[/tex]

Thanks for any help.