John's copy of Gaussian elimination to solve a 3x3 system of linear equations

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John Steele 5 years, 11 months ago

Created this as a copy of Gaussian elimination to solve a 3x3 system of linear equations.

Name	Status	Author	Last Modified
Gauss elimination to solve a system of linear equations.	Ready to use	Newcastle University Mathematics and Statistics	30/11/2020 16:34
Henrik Skov's copy of Gauss elimination to solve a sytem of linear equations	draft	Henrik Skov Midtiby	07/07/2016 11:32
2.1 Introduction to solving systems of linear equations	draft	Christian Saemann	15/09/2016 13:57
Simon's copy of Gauss elimination to solve a sytem of linear equations	draft	Simon Vaughan	09/11/2016 16:37
Alex's copy of Simon's copy of Gauss elimination to solve a sytem of linear equations	draft	Alex Van den Hof	26/01/2017 14:17
Ch10 Q4	draft	Alex Van den Hof	20/02/2017 16:02
Gaussian elimination to solve a 3x3 system of linear equations	draft	Violeta CIT	11/10/2018 17:06
Gaussian elimination to solve a 3x3 system of linear equations	draft	Marie Nicholson	04/02/2021 15:47
Praneetha's copy of Gaussian elimination to solve a 3x3 system of linear equations	draft	Praneetha Singh	28/06/2018 05:20
Gaussian elimination to solve a 3x3 system of linear equations	Needs to be tested	Violeta CIT	08/11/2018 14:31
Gaussian elimination to solve a 3x3 system of linear equations	draft	Marie Nicholson	11/10/2018 17:06
Sarah's copy of Gaussian elimination to solve a 3x3 system of linear equations	draft	Sarah Barns	11/10/2018 23:55
John's copy of Gaussian elimination to solve a 3x3 system of linear equations	draft	John Steele	13/05/2019 03:59
Maria's copy of John's copy of Gaussian elimination to solve a 3x3 system of linear equations	draft	Maria Aneiros	24/05/2019 00:01
Simon's copy of Gauss elimination to solve a system of linear equations.	draft	Simon Thomas	12/06/2019 11:51
Gauss elimination to solve a system of linear equations.	draft	Xiaodan Leng	10/07/2019 22:52

There are 31 other versions that do you not have access to.

Question statement

Solve the system of equations using Gauss 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
c	integer	2
b	integer	3
c3	integer	1
c2	integer	2
y	number	-662
x	number	322
c1	integer	3
z	number	111

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random(2..6)

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Generated value: `integer`

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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.	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.

Give a worked solution to the whole question.

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John's copy of Gaussian elimination to solve a 3x3 system of linear equations

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Taxonomy: mathcentre

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John Steele 5 years, 11 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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John's copy of Gaussian elimination to solve a 3x3 system of linear equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

John Steele 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`