EG5116 EG4103 Matrices: Cramers Rule applied to 3 simultaneous equations

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bryan pearce

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bryan pearce 8 years, 2 months ago

Created this as a copy of EG3101 EG5116 EG4103 Matrices: cofactors determinant and inverse of a 3x3 matrix.

Name	Status	Author	Last Modified
Multiply two matrices	Ready to use	Christian Lawson-Perfect	01/06/2016 11:06
Lois's copy of Multiply two matrices	draft	Lois Rollings	26/08/2016 11:46
Simon's copy of Lois's copy of Multiply two matrices	draft	Simon Vaughan	25/01/2017 14:35
Francis 's copy of Simon's copy of Lois's copy of Multiply two matrices	draft	Francis Duah	22/11/2016 23:11
Francis 's copy of Francis 's copy of Simon's copy of Lois's copy of Multiply two matrices	draft	Francis Duah	22/11/2016 23:13
EG3101 EG5116 EG4103 Matrices: Multiplying two 2x2 matrices	draft	bryan pearce	12/01/2017 14:38
EG3101 EG5116 EG4103 Matrices: Multiplying two 3x3 matrices	draft	bryan pearce	12/01/2017 15:11
EG3101 EG5116 EG4103 Matrices: adding and subtracting two 3x3 matrices	draft	bryan pearce	18/10/2017 17:58
EG3101 EG5116 EG4103 Matrices: determinant and inverse of a 2x2 matrix	draft	bryan pearce	12/01/2017 16:53
EG3101 EG5116 EG4103 Matrices: cofactors determinant and inverse of a 3x3 matrix	draft	bryan pearce	17/01/2017 12:38
EG5116 EG4103 Matrices: Cramers Rule applied to 3 simultaneous equations	draft	bryan pearce	20/01/2017 17:56
Denis's copy of EG5116 EG4103 Matrices: Cramers Rule applied to 3 simultaneous equations	draft	Denis Flynn	23/03/2020 16:46
Alex's copy of Simon's copy of Lois's copy of Multiply two matrices	draft	Alex Van den Hof	26/01/2017 14:17
Owen's copy of Multiply two matrices	draft	Owen Jepps	31/03/2020 08:21
Andrew's copy of Matrices: Cramers Rule 3x3	draft	Andrew Dunbar	30/06/2017 20:34
Andrew's copy of Matrices: Cramers Rule 3x3	draft	Andrew Dunbar	30/06/2017 22:04
Ex Sheet 6 Cofactors, Determinant and inverse of a 3x3 matrix	draft	Violeta CIT	21/09/2017 19:19
Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix	Ready to use	Violeta CIT	04/10/2017 16:45
Question 5 MATH6005 Assessment 1 Cofactors, Determinant and Inverse of a 3x3 matrix	Ready to use	Violeta CIT	04/10/2017 17:56
Week 13: Matrices: Cramers Rule 3x3	draft	Ashley Cusack	12/12/2017 14:37
Pelle's copy of Ashley's copy of Andrew's copy of Matrices: Cramers Rule 3x3	Ready to use	Pelle Englund	10/12/2021 19:02
Marisa's copy of Week 13: Matrices: Cramers Rule 3x3	draft	Marisa Llorens	17/01/2018 12:42
Adrian's copy Matrices: adding and subtracting two 3x3 matrices	draft	Adrian Jannetta	16/08/2023 14:56
Matrices: adding and subtracting two 3x3 matrices	draft	Marie Nicholson	04/02/2021 15:44
Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix	Ready to use	Violeta CIT	16/09/2018 12:34
Cofactors, Determinant and Inverse of a 3x3 matrix (Adaptive)	Ready to use	Clodagh Carroll	27/09/2019 13:37
Custom Marking version of Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix (CC)	Doesn't work	Clodagh Carroll	27/09/2018 17:08
William's copy of Multiply two matrices	draft	William Lee	18/12/2018 13:00
Alison's copy of Matrices: cofactors determinant and inverse of a 3x3 matrix	draft	Alison Loddick	29/01/2019 08:38
Lois's copy of Multiply two matrices	draft	Lois Rollings	05/06/2019 16:06
Cofactors, Determinant and Inverse of a 3x3 matrix	draft	Xiaodan Leng	10/07/2019 23:30
Paula's copy of Adaptive Marking version of Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix (CC)	draft	Paula Ruiz-Hincapie	04/09/2019 11:14
Matt's copy of Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix	draft	Matt Tranter	16/09/2019 12:29
W1b - Cofactors, Determinant and Inverse of a 3x3 matrix	Ready to use	Timur Zaripov	17/06/2022 09:37
Cofactors, Determinant and Inverse of a 3x3 matrix (Adaptive) draft 2	draft	Clodagh Carroll	25/09/2020 14:45
Cramers Rule 3x3	draft	Shaheen Charlwood	19/02/2020 21:34
Andrew's copy of Multiply two matrices	Ready to use	Andrew Hogue	22/06/2020 17:12
Inverse of a 3x3 matrix	draft	Tamsin Smith	17/09/2024 13:21

There are 71 other versions that do you not have access to.

Question statement

Using Cramer's rule , solve the system of equations:

$\var{a11}x_1+\var{a12}x_2+\var{a13}x_3=\var{c1}$

$\var{a21}x_1+\var{a22}x_2+\var{a23}x_3=\var{c2}$

$\var{a31}x_1+\var{a32}x_2+\var{a33}x_3=\var{c3}$

Give any introductory information the student needs.

			Name	Type	Generated Value

matrixA1	matrix	Matrix of size 3×3
matrixA2	matrix	Matrix of size 3×3
matrixA3	matrix	Matrix of size 3×3

			Name	Type	Generated Value

matrixA	matrix	Matrix of size 3×3
a11	rational	47/10
a12	rational	1
a21	rational	17/10
a22	rational	41/10
a13	rational	37/5
a23	rational	23/10
a31	rational	36/5
a32	rational	0
a33	rational	49/10
x1	rational	13/10
x2	rational	-1/2
x3	rational	-11/10
c1	rational	-253/100
c2	rational	-237/100
c3	rational	397/100

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
matrix([c1,a12,a13],[c2,a22,a23],[c3,a32,a33])

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: `matrix`

matrix([-2.53,1,7.4],[-2.37,4.1,2.3],[3.97,0,4.9])

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→ Used by:

"Part b)" → "Gap 0." - Minimum accepted value
"Part b)" → "Gap 0." - Maximum accepted value

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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

What is the determinant of A= $\var{matrixA}$ ? i.e $\Delta_0$

Unnamed gap

Advice

$A=\left( \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{array} \right),$

$C=\left( \begin{array}{ccc} c_{1} \\ c_{2} \\c_{3} \end{array} \right),$

Cramer's Rule : ${x_1}=\frac{\Delta_1}{\Delta_0}$ , ${x_2}=\frac{\Delta_2}{\Delta_0}$ , ${x_3}=\frac{\Delta_3}{\Delta_0}$

Where:

$\Delta_0=\left| \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{array} \right|$

$\Delta_1=\left| \begin{array}{ccc} c_{1} & a_{12} & a_{13} \\c_{2} & a_{22} & a_{23}\\ c_{3} & a_{32} & a_{33}\end{array} \right|$

$\Delta_2=\left| \begin{array}{ccc} a_{11} & c_{1} & a_{13} \\a_{21} & c_{2} & a_{23}\\ a_{31} & c_{3} & a_{33}\end{array} \right|$

$\Delta_3=\left| \begin{array}{ccc} a_{11} & a_{12} & c_{1} \\a_{21} & a_{22} & c_{2}\\ a_{31} & a_{32} & c_{3}\end{array} \right|$

Give a worked solution to the whole question.

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This question is used in the following exam:

EG5116 EG4103 Matrices by bryan pearce in bryan's workspace.

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EG5116 EG4103 Matrices: Cramers Rule applied to 3 simultaneous equations

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Taxonomy: mathcentre

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bryan pearce 8 years, 2 months ago

Error in variable testing condition

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Generated value: `matrix`

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EG5116 EG4103 Matrices: Cramers Rule applied to 3 simultaneous equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

bryan pearce 8 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: matrix

Parts

Gap-fill

Generated value: `matrix`