MA4100 4.4 Gaussian Elimination

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James Denholm-Price

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James Denholm-Price

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Ready to use

9 years, 11 months ago

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James Denholm-Price 9 years, 11 months ago

Gave some feedback: Ready to use

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James Denholm-Price 10 years, 3 months ago

Created this as a copy of Gauss Elimination - practice version.

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	2
b	integer	3
c	integer	3
c1	integer	3
c2	integer	1
c3	integer	2
y	number	-33
x	number	47
z	number	18

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..6)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Statement
"Part a)" → "Gap 3." - Minimum accepted value
"Part a)" → "Gap 3." - Maximum accepted value
"Part a)" → "Gap 5." - Minimum accepted value
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"Part a)" → "Gap 9." - Minimum accepted value
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"Part b)" - prompt
"Part b)" → "Gap 4." - Minimum accepted value
"Part b)" → "Gap 4." - Maximum accepted value
"Part b)" → "Gap 5." - Minimum accepted value
"Part b)" → "Gap 5." - Maximum accepted value
"Part b)" → "Gap 7." - Minimum accepted value
"Part b)" → "Gap 7." - Maximum accepted value
"Part c)" - prompt
"Part c)" → "Gap 1." - Minimum accepted value
"Part c)" → "Gap 1." - Maximum accepted value
"Part c)" → "Gap 2." - Minimum accepted value
"Part c)" → "Gap 2." - Maximum accepted value
"Part c)" → "Gap 4." - Minimum accepted value
"Part c)" → "Gap 4." - Maximum accepted value
"Part d)" - prompt

Parts

Part a) Gap-fill
1. Gap Gap 0. Choose one from a list
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Part d) Gap-fill
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Gap-fill

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.
WHY? Choose one of the following:
Gap 0.

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.	$\left) \begin{matrix} \phantom{.} \\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \end{matrix} \right.$
	Gap 5.	Gap 6.	Gap 7.		Gap 8.
	Gap 9.	Gap 10.	Gap 11.		Gap 12.

Advice

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

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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This question is used in the following exams:

MA4100 Gaussian Elimination part 2 of 3 - echelon form by James Denholm-Price in MA4100.
My first exam by Rob Wilson in Rob's workspace.
Row echelon form by Philip Walker in MATH1060.
Test exam by Brook Galna in Brook's workspace.
Estelle_numbas_create_basket by Estelle Drysdale in Estelle's workspace.

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James Denholm-Price 9 years, 11 months ago

James Denholm-Price 10 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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MA4100 4.4 Gaussian Elimination

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

James Denholm-Price 9 years, 11 months ago

James Denholm-Price 10 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`