My Math Forum Algebraic Properties of Matrix Operations

 Linear Algebra Linear Algebra Math Forum

 October 1st, 2009, 02:42 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, 03:27 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, 04:36 PM #3 Newbie   Joined: Oct 2009 Posts: 20 Thanks: 0 Re: Algebraic Properties of Matrix Operations Thanks parasio
 October 3rd, 2009, 01:43 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.

 Tags algebraic, matrix, operations, properties

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post kelseyallen77 Linear Algebra 1 November 4th, 2013 10:30 AM questioner1 Linear Algebra 3 August 16th, 2012 09:03 AM Nexusfactor Linear Algebra 1 February 12th, 2012 03:16 AM supernerd707 Algebra 1 March 18th, 2011 01:32 PM geyikrali Linear Algebra 2 January 26th, 2009 12:12 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top