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 October 1st, 2009, 01:42 PM #1 Newbie   Joined: Oct 2009 Posts: 20 Thanks: 0 Algebraic Properties of Matrix Operations Show that if x1 and x2 are solutions to the linear system Ax=b, then x1-x2 is a solution to the associated homogeneous system Ax=0.
 October 1st, 2009, 02:27 PM #2 Senior Member   Joined: Feb 2009 Posts: 172 Thanks: 5 Re: Algebraic Properties of Matrix Operations Let $x_1$ and $x_2$ be solutions to $Ax=b$. Then $Ax_1=b$ and $Ax_2=b$. Hence, $Ax_1-Ax_2=b-b-0$. Since, $A$ is a linear transformation $Ax_1-Ax_2=A(x_1-x_2)$. Hence $A(x_1-x_2)=0$ that is $x_1-x_2$ is a solution to $Ax=0$.
 October 2nd, 2009, 03:36 PM #3 Newbie   Joined: Oct 2009 Posts: 20 Thanks: 0 Re: Algebraic Properties of Matrix Operations Thanks parasio
 October 3rd, 2009, 12:43 AM #4 Senior Member   Joined: Feb 2009 Posts: 172 Thanks: 5 Re: Algebraic Properties of Matrix Operations You're welcome. If you need anything just write to me.

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