# Quiz Question...... HELP!!!

• Sep 25th 2006, 06:32 AM
TreeMoney
Quiz Question...... HELP!!!
The question is.....

Let u be a solution to Ax = b and v be a solution to Ax = 0, where A is an m x n matrix and b is a vector in R^m. Show that u + v is also a solution to Ax = b.

To be honest, I don't even know where to start. This was a quiz question on a quiz in my linear algebra class. I thought I had gotten it right, or at least mostly correct. But I got no credit for it whats so ever. Please explain how to do this.

TIA
John
• Sep 25th 2006, 06:40 AM
topsquark
Quote:

Originally Posted by TreeMoney
The question is.....

Let u be a solution to Ax = b and v be a solution to Ax = 0, where A is an m x n matrix and b is a vector in R^m. Show that u + v is also a solution to Ax = b.

To be honest, I don't even know where to start. This was a quiz question on a quiz in my linear algebra class. I thought I had gotten it right, or at least mostly correct. But I got no credit for it whats so ever. Please explain how to do this.

TIA
John

Assume your givens above. Recall that matrix multiplication distributes over matrix/vector addition.

Let x = u + v
Then Ax = A(u + v) = Au + Av = b + 0 = b. (Check!)

-Dan