Gaussian elimination to solve a system of linear equations - Introductory

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From users who are members of Linear Algebra 1st year :

Tatiana Tyukina	said	Ready to use	4 years, 8 months ago
Julia Goedecke	said	Needs to be tested	4 years, 8 months ago

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Julia Goedecke 4 years, 8 months ago

Published this.

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Tatiana Tyukina 4 years, 8 months ago

Gave some feedback: Ready to use

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Julia Goedecke commented 4 years, 8 months ago

Combined the last two parts into one with some automatic fills of some of the gaps. Put the marks of the parts in.

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Julia Goedecke 4 years, 8 months ago

Gave some feedback: Needs to be tested

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Julia Goedecke 4 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Gaussian elimination to solve a system of linear equations - Introductory	Ready to use	Julia Goedecke	25/08/2021 12:57
Gaussian elimination to solve a system of linear equations - scaffolded	Ready to use	Julia Goedecke	25/08/2021 12:57
Gaussian elimination to solve a system of equations	Ready to use	Andrew Brown	12/09/2022 14:48
Gaussian elimination to solve a system of linear equations	Ready to use	Andrew Brown	12/09/2022 14:48

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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 column below the second entry in the second row using the second row.
Part d) Introduce zeros in the third column above the third entry in the third row using the third row.
Part e) Introduce zeros in the second column above the second entry in the second row using the second row.
Also read off the solution to the system.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
c	integer	1
b	integer	4
c3	integer	1
c2	integer	3
y	number	1
x	number	1
c1	integer	5
z	number	-1

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
"Part a)" → "Gap 5." - Maximum accepted value
"Part a)" → "Gap 6." - Minimum accepted value
"Part a)" → "Gap 6." - Maximum accepted value
"Part a)" → "Gap 7." - Minimum accepted value
"Part a)" → "Gap 7." - Maximum accepted value
"Part a)" → "Gap 9." - Minimum accepted value
"Part a)" → "Gap 9." - Maximum accepted value
"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)" → "Gap 1." - Minimum accepted value
"Part d)" → "Gap 1." - Maximum accepted value
"Part d)" → "Gap 2." - Minimum accepted value
"Part d)" → "Gap 2." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Choose one from a list
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Part b) Gap-fill
1. Gap Gap 0. Number entry
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Part c) Gap-fill
1. Gap Gap 0. Number entry
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Part d) Gap-fill
1. Gap Gap 0 Number entry
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6. Gap Gap 5. Number entry
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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.

$\left( \begin{matrix} \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{,}\end{matrix} \right.$	Gap 1.	Gap 2.	Gap 3.	$\left. \begin{matrix} \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\end{matrix} \middle\| \begin{matrix} \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\end{matrix} \right.$	Gap 4.	$\left) \begin{matrix} \phantom{.} \\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.} \end{matrix} \right.$
	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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Gaussian elimination to solve a system of linear equations - Introductory

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Julia Goedecke 4 years, 8 months ago

Tatiana Tyukina 4 years, 8 months ago

Julia Goedecke commented 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Gaussian elimination to solve a system of linear equations - Introductory

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Julia Goedecke 4 years, 8 months ago

Tatiana Tyukina 4 years, 8 months ago

Julia Goedecke commented 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`