Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix

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Violeta CIT 7 years, 5 months ago

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Created this as a copy of Ex Sheet 6 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

Give any introductory information the student needs.

			Name	Type	Generated Value

cof11	integer	18
cof12	integer	-40
cof13	integer	8
cof21	integer	-6
cof22	integer	0
cof23	integer	0
cof31	integer	6
cof32	integer	-12
cof33	integer	0

			Name	Type	Generated Value

			Name	Type	Generated Value

matrixA	matrix	Matrix of size 3×3
a11	integer	0
a12	integer	0
a21	integer	4
a22	integer	2
a13	integer	-3
a23	integer	1
a31	integer	0
a32	integer	2
a33	integer	10
inverseA	matrix	Matrix of size 3×3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
a22*a33-a32*a23

JME function reference

Description

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Generated value: `integer`

← Depends on:

→ Used by:

inverseA

This variable doesn't seem to be used anywhere.

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

Calculate the nine cofactors of A= $\var{matrixA}$ ?

$A _{11}$ cofactor in position 1,1Gap 0.

$A_{12}$ cofactor in position 1,2Gap 1.

$A_{13}$ cofactor in position 1,3Gap 2.

$A_{21}$ cofactor in position 2,1Gap 3.

$A_{22}$ cofactor in position 2,2Gap 4.

$A_{23}$ cofactor in position 2,3Gap 5.

$A_{31}$ cofactor in position 3,1Gap 6.

$A_{32}$ cofactor in position 3,2Gap 7.

$A_{33}$ cofactor in position 3,3Gap 8.

Advice

$A=\left( \begin{array}{ccc} a & b & c \\d & e&f\\ g&h&j \end{array} \right),$

Cofactors are given by

$A=\left( \begin{array}{ccc} a & b & c \\d & e&f\\ g&h&j \end{array} \right),$

Cof11 =

$+\left| \begin{array}{ccc} e&f\\ h&j \end{array} \right|,$

Cof12 =

$-\left| \begin{array}{ccc} d & f\\ g&j \end{array} \right|,$

Cof13 =

$+\left| \begin{array}{ccc} d & e\ g&h\end{array} \right|,$

Cof21 =

$-\left| \begin{array}{ccc} b & c \\h&j \end{array} \right|,$

Cof22 =

$+\left| \begin{array}{ccc} a & c \\ g&j \end{array} \right|,$

Cof23 =

$-\left| \begin{array}{ccc} a & b \\g&h\end{array} \right|,$

Cof31 =

$+=\left| \begin{array}{ccc} b & c \\e&f\end{array} \right|,$

Cof32 =

$-\left| \begin{array}{ccc} a & c \\d & f\end{array} \right|,$

Cof33 =

$+\left| \begin{array}{ccc} a & b\\d & e \end{array} \right|,$

Then, the determinant of A is given by the sum of the product of any row ( or column) elements by their cofactors

e.g row 1 determinant = a*cof11+b*cof12+c*cof13

and the inverse of A is given by the ratio of the adjoint(A) and the deteminant of A

where adjoint A= \left(

$\begin{array}{ccc} cof11 & cof21 & cof31 \\cof12 & cof22&cof32\\ cof13&cof23&cof33 \end{array}$ \right),\]

inverse of A=

$\frac{1}{det(A)}*\left( \begin{array}{ccc} cof11 & cof21 & cof31 \\cof12 & cof22&cof32\\ cof13&cof23&cof33 \end{array} \right),$

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Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix

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Violeta CIT 7 years, 5 months ago

Violeta CIT 7 years, 6 months ago

Violeta CIT 7 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Violeta CIT 7 years, 5 months ago

Violeta CIT 7 years, 6 months ago

Violeta CIT 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`