Gaussian Elimination

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John Sheekey

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John Sheekey 7 years, 1 month ago

Created this as a copy of MA4100 4.4 Gaussian Elimination.

Name	Status	Author	Last Modified
MA4100 4.4 Gaussian Elimination	Ready to use	James Denholm-Price	01/06/2016 11:45
Habiba's copy of MA4100 4.4 Gaussian Elimination	Ready to use	Habiba Gora	01/06/2016 09:47
delete syntax checkinbg bryan's copy of MA4100 4.4 Gaussian Elimination	Ready to use	bryan pearce	24/09/2016 21:14
E1 Q1: Gaussian Elimination	Ready to use	Thomas Winyard	05/01/2022 22:01
Gaussian Elimination (2)	draft	John Sheekey	09/02/2018 16:50
John's copy of MA4100 4.4 Gaussian Elimination	draft	John Sheekey	09/02/2018 16:46
Gaussian Elimination	draft	John Sheekey	09/02/2018 16:49
Gaussian Elimination	draft	Andrew Iskauskas	26/06/2018 20:29
Praneetha's copy of Gaussian Elimination	draft	Praneetha Singh	28/06/2018 05:19
James's copy of MA4100 4.4 Gaussian Elimination	draft	James Gaunt	29/03/2019 16:50
Gaussian Elimination	draft	Xiaodan Leng	11/07/2019 00:57
Gaussian Elimination	draft	Xiaodan Leng	11/07/2019 06:20

There are 19 other versions that do you not have access to.

Question statement

Solve the system of equations using Gaussian Elimination

$\begin{eqnarray*} &\var{a}x&+\;&\var{a*b-1}y&+\;\var{a^2*b-a-a*b}z&=&\var{c2}\\ &\var{a*c}x&+\;&\var{c*b}y&+\;z&=&\var{c1}\\ &x&+\;&\var{b}y&+\;\var{b*a-b}z&=&\var{c3} \end{eqnarray*}$
Part a) Rearrange the order of the equations and represent this as a system of equations using a matrix.
Part b) Introduce zeros in the first column using the first row.
Part c) Introduce zeros in the second coumn below the second entry in the second row using the second row.
Also need to solve for

$z$ using the last row of the reduced matrix.
Part d) Solve for

$y$ and

$x$ using the second and first rows of the reduced matrix.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
b	integer	4
c	integer	3
c1	integer	2
c2	integer	3
c3	integer	2
y	number	-3027
x	number	1990
z	number	506

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..6)

JME function reference

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Generated value: `integer`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
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Ask the student a question, and give any hints about how they should answer this part.

Re-arrange the rows so that the third row becomes the first row, the first the second and the second the third.

Now write down the entries of the matrix you will use for Gaussian Elimination, remember to include the constants as the last column.

$\left( \begin{matrix} \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \end{matrix} \right.$	Gap 1.	Gap 2.	Gap 3.	$\left\| \begin{matrix} \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \end{matrix} \right.$	Gap 4.	$\left) \begin{matrix} \phantom{.} \\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \end{matrix} \right.$
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	Gap 9.	Gap 10.	Gap 11.		Gap 12.

Advice

Look at the revealed answers for this question. All the information needed is there.

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This question is not used in any exams.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

John Sheekey 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Gaussian Elimination

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

John Sheekey 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`