Cofactors, Determinant and Inverse of a 3x3 matrix

Error

There was an error loading the page.

Contributors

History

○

Xiaodan Leng 5 years, 8 months ago

Created this as a copy of Ex 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	54
cof12	integer	-106
cof13	integer	-10
cof21	integer	-28
cof22	integer	2
cof23	integer	10
cof31	integer	-22
cof32	integer	48
cof33	integer	-20

			Name	Type	Generated Value

			Name	Type	Generated Value

matrixA	matrix	Matrix of size 3×3
a11	integer	2
a12	integer	3
a21	integer	10
a22	integer	5
a13	integer	5
a23	integer	1
a31	integer	4
a32	integer	1
a33	integer	11
inverseA	matrix	Matrix of size 3×3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
a22*a33-a32*a23

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`

← Depends on:

→ Used by:

inverseA

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Matrix entry
  Add

Gap-fill

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=

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

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:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Cofactors, Determinant and Inverse of a 3x3 matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Cofactors, Determinant and Inverse of a 3x3 matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`