Introduction to Matlab - Revision history

Admin at 22:41, 15 October 2010

2010-10-15T22:41:39Z

← Older revision		Revision as of 22:41, 15 October 2010
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	<math>		<math>
	\begin{~~array~~}		\begin{align}
	3x + 5y - 2z &=& 4 \\		3x + 5y - 2z &=& 4 \\
	3(2)+0-2z &=& 4 \\		3(2)+0-2z &=& 4 \\
	-2z &=& -2		-2z &=& -2
	\end{~~array~~}		\end{align}
	</math>		</math>

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	\end{array}		\end{array}
	\right]		\right]
	<math>		</math>

	If we swapped column 1 and column 2, how would we have to change the unknowns vector?		If we swapped column 1 and column 2, how would we have to change the unknowns vector?
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	\end{array}		\end{array}
	\right]		\right]
			</math>

Admin: /* Solving Systems of Equations */

2010-10-15T22:40:41Z

Solving Systems of Equations

← Older revision		Revision as of 22:40, 15 October 2010
Line 554:		Line 554:
	<math>		<math>
	\begin{array}		\begin{array}
	3x + 5y - 2z = 4 \\		3x + 5y - 2z &=& 4 \\
	3(2)+0-2z = 4		3(2)+0-2z &=& 4 \\
	-2z = -2		-2z &=& -2
	\end{array}		\end{array}
	</math>		</math>

Admin at 22:17, 15 October 2010

2010-10-15T22:17:53Z

← Older revision		Revision as of 22:17, 15 October 2010
Line 532:		Line 532:
	</math>		</math>

			Next, we want an equation with ''two'' unknowns: y, and something else

			Let's try (3) + 2*(2):

			<math>
			\begin{align}
			3x + 5y - 2z &=& 4 \\
			\underline{ +2( -2x - 6y + z ) } &=& \underline{-3} \\
			-x - 7y + 0z &=& -2
			\end{align}
			</math>

			Next when we plug in <math>y=0</math> we get

			<math>
			x = 2
			</math>

			Finally, we want an equation with ''all 3'' unknowns, so that we can plug in the values for x and y that we just found

			<math>
			\begin{array}
			3x + 5y - 2z = 4 \\
			3(2)+0-2z = 4
			-2z = -2
			\end{array}
			</math>

			so,

			<math>
			z = 1
			</math>

			What happened to our matrix? What did our matrix become?

			Did row 1 change?

			Did row 2 change?

			For the first step, we transformed row (3) into row(3) + row(2) - row(1)

			<math>
			\left[
			\begin{array}{ccc}
			1 & 3 & -1 \\
			-2 & -6 & 1 \\
			3 & 5 & -2
			\end{array}
			\right]

			\rightarrow

			\left[
			\begin{array}{ccc}
			1 & 3 & -1 \\
			-2 & -6 & 1 \\
			0 & -4 & 0
			\end{array}
			\right]
			</math>

			What happened in the second step?

			Row(2) changed to row(3) + 2*row(2)

			<math>
			\left[
			\begin{array}{ccc}
			1 & 3 & -1 \\
			-2 & -6 & 1 \\
			0 & -4 & 0
			\end{array}
			\right]

			\rightarrow

			\left[
			\begin{array}{ccc}
			1 & 3 & -1 \\
			-1 & -7 & 0 \\
			0 & -4 & 0
			\end{array}
			\right]
			</math>

			or, we could swap column 1 and column 2 and rewrite this as:

			<math>
			\left[
			\begin{array}{ccc}
			3 & 1 & -1 \\
			-7 & -1 & 0 \\
			-4 & 0 & 0
			\end{array}
			\right]
			<math>

			If we swapped column 1 and column 2, how would we have to change the unknowns vector?

			<math>
			\left[
			\begin{array}{c}
			x \\
			y \\
			z
			\end{array}
			\right]

			\rightarrow

			\left[
			\begin{array}{c}
			y \\
			x \\
			z
			\end{array}
			\right]

Admin: /* Solving Systems of Equations */

2010-10-15T22:06:28Z

Solving Systems of Equations

← Older revision		Revision as of 22:06, 15 October 2010
Line 261:		Line 261:
	-2y &=& -2 \\		-2y &=& -2 \\
	y &=& 1		y &=& 1
			\end{align}
	</math>		</math>

Admin at 22:05, 15 October 2010

2010-10-15T22:05:51Z

@@ Line 440: / Line 440: @@
 -\frac{14}{4} + 4y &=& 1 \\
 y &=& \frac{4}{4} + \frac{14}{4} = \frac{18}{4} \\
 \end{align}
 </math>

Admin at 21:58, 15 October 2010

2010-10-15T21:58:33Z

Show changes

Admin: moved Lecture:Introduction to Matlab to Introduction to Matlab

2010-10-15T21:37:46Z

moved Lecture:Introduction to Matlab to Introduction to Matlab

← Older revision	Revision as of 21:37, 15 October 2010
(No difference)

Admin at 20:18, 15 October 2010

2010-10-15T20:18:24Z

← Older revision		Revision as of 20:18, 15 October 2010
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	__TOC__		__TOC__

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	The matrix representation is really easy		The matrix representation is really easy





			[[Category:Lectures]]

Admin: /* 1703 Lecture: Introduction to Matlab */

2010-10-15T20:00:10Z

1703 Lecture: Introduction to Matlab

← Older revision		Revision as of 20:00, 15 October 2010
Line 1:		Line 1:

			__TOC__

	= 1703 Lecture: Introduction to Matlab =		= 1703 Lecture: Introduction to Matlab =

Admin: /* Matrix Representation */

2010-10-15T19:59:29Z

Matrix Representation

← Older revision		Revision as of 19:59, 15 October 2010
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	\left[		\left[
	\begin{array}{cc}		\begin{array}{c}
	x \\		x \\
	y		y
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	\left[		\left[
	\begin{array}{cc}		\begin{array}{c}
	1 \\		1 \\
	11		11
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	<math>		<math>
	\left[		\left[
	\begin{array}{cc}		\begin{array}{ccc}
	3 & 5 & 1 \\		3 & 5 & 1 \\
	2 & -1 & -1 \\		2 & -1 & -1 \\
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	\left[		\left[
	\begin{array}{cc}		\begin{array}{c}
	x \\		x \\
	y \\		y \\
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	\left[		\left[
	\begin{array}{cc}		\begin{array}{c}
	16 \\		16 \\
	3 \\		3 \\