Inverse of a 2x2 Matrix

Error

There was an error loading the page.

Contributors

Frank Doheny

Feedback

From users who are members of Matrices :

Frank Doheny

said

Ready to use

8 years ago

History

○

Frank Doheny 8 years ago

Gave some feedback: Ready to use

○

Frank Doheny 8 years ago

Created this as a copy of Matrix Multiplication.

Name	Status	Author	Last Modified
Matrix Multiplication 1	Ready to use	Bill Foster	01/06/2016 09:47
Eva's copy of Matrix Multiplication 1	Ready to use	Eva Szatmari	01/06/2016 09:47
Multiplicación de matrices 001	Ready to use	Jos Klenner	02/12/2020 15:42
Lois's copy of Matrix Multiplication 1	Ready to use	Lois Rollings	27/07/2016 10:50
Julie's copy of Matrix Multiplication 1	Ready to use	Julie Crowley	26/07/2016 12:53
Katie's copy of Matrix Multiplication 1	Ready to use	Katie Dexter	01/06/2016 09:47
Andrew's copy of Katie's copy of Matrix Multiplication 1	Ready to use	Andrew Iskauskas	01/06/2016 09:47
Andrew's copy of Andrew's copy of Katie's copy of Matrix Multiplication 1	Ready to use	Andrew Dunbar	01/06/2016 09:47
JUSTYNA's copy of Katie's copy of Matrix Multiplication 1	Ready to use	JUSTYNA NOWICZ	01/06/2016 09:47
Simon's copy of Lois's copy of Matrix Multiplication 1	draft	Simon Vaughan	09/11/2016 16:37
Alex's copy of Simon's copy of Lois's copy of Matrix Multiplication 1	draft	Alex Van den Hof	26/01/2017 14:17
Matrices: Multiplication 1	draft	Clare Lundon	04/03/2019 14:50
Matrix Multiplication	Ready to use	Frank Doheny	14/03/2018 21:05
Inverse of a 2x2 Matrix	Ready to use	Frank Doheny	14/03/2018 21:04
Andrew's copy of Matrices: Multiplication 1	draft	Andrew Dunbar	30/06/2017 22:04
Ex 2 Matrix Multiplication 1 (2x2 matrices)	draft	Violeta CIT	11/09/2017 10:47
Mark's copy of Inverse of a 2x2 Matrix	draft	Mark Hodds	07/09/2017 14:58
MATH6058 Matrix Multiplication 1 (2x2 matrices)	draft	Catherine Palmer	09/03/2023 19:52
Clodagh's copy of MATH6058 Matrix Multiplication 1 (2x2 matrices)	draft	Clodagh Carroll	26/09/2017 10:29
Question 2 MATH 6005 Assessment 1 Matrix Multiplication 1 (2x2 matrices)	Ready to use	Violeta CIT	04/10/2017 17:55
Question 2.1 MATH 6005 Assessment 1 Matrix Multiplication 2 (3x3 by 3x2 matrices)	Ready to use	Violeta CIT	17/06/2019 11:24
Ioannis's copy of Lois's copy of Matrix Multiplication 1	draft	Ioannis Lignos	28/10/2018 20:44
Matrices: Multiplication	draft	Clare Lundon	03/11/2017 16:44
Matrix Multiplication 1 (2x2 matrices)	draft	Marie Nicholson	04/02/2021 15:44
Matrix Multiplication (2x2)	draft	Marie Nicholson	04/02/2021 15:34
Joseph's copy of Matrix Multiplication 1	draft	Joseph Clarke	15/06/2018 14:25
Joseph's copy of Matrix Multiplication 1	draft	Antonia Wilmot-Smith	31/08/2018 12:23
Ex 2 Matrix Multiplication 1 (2x2 matrices)	Ready to use	Violeta CIT	16/09/2018 11:10
William's copy of Question 2.1 MATH 6005 Assessment 1 Matrix Multiplication 2 (3x3 by 3x2 matrices)	draft	William Lee	12/10/2018 15:03
Simon's copy of Matrix Multiplication 1	draft	Simon Thomas	01/04/2019 12:12
Quiz copy of Matrix Multiplication 1 (2x2 matrices)	draft	Marie Nicholson	07/05/2021 14:34
John's copy of Ex 2 Matrix Multiplication 1 (2x2 matrices)	draft	John Steele	13/05/2019 03:59
John's copy of Matrix Multiplication	draft	John Steele	13/05/2019 03:58
Josh's copy of Question 2.1 MATH 6005 Assessment 1 Matrix Multiplication 2 (3x3 by 3x2 matrices)	draft	Josh Lim	19/06/2019 16:35
Matrix Multiplication 2 (3x3 by 3x2 matrices)	draft	Xiaodan Leng	10/07/2019 21:35
Anthony's copy of Matrix Multiplication 1	draft	Anthony Brown	17/08/2019 10:43
Matrix Multiplication	draft	Thomas Waters	11/09/2019 21:34
Matrix Multiplication (2x3 by 3x2 matrices)	draft	Marie Nicholson	26/09/2019 12:29
L1 - Matrix Multiplication (2x3 by 3x2 matrices)	Ready to use	Timur Zaripov	17/06/2022 09:37
L1 - Matrix Multiplication (1x3 by 3x1 matrices)	Ready to use	Timur Zaripov	17/06/2022 09:37
Matrix Multiplication	draft	Shaheen Charlwood	19/02/2020 21:15
Matrix Multiplication	draft	Tamsin Smith	17/09/2024 13:11

There are 49 other versions that do you not have access to.

Question statement

Given the matrix:

$\mathbf{A}=\begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a11	integer	5
a12	integer	4
a21	integer	46
a22	integer	37
k	integer	9
det	integer	1
b11	rational	37
b12	rational	-4
b21	rational	-46
b22	rational	5
c	integer	1
r	integer	65
s	integer	600
r1	integer	5
s1	integer	10

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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
Advice
"Part b)" - prompt

Parts

Part a) Gap-fill
1. Gap Matrix entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

Determine the inverse matrix $\mathbf{A^{-1}}$

Input the exact values of the entries in to the matrix.

$\mathbf{A^{-1}}$ = Unnamed gap

Advice

Given a matrix $\mathbf{A}=\begin{pmatrix} a & b\\ c & d\\ \end{pmatrix}$

The determinant of the matrix is given by: $|\mathbf{A}|=ad-bc$

$\mathbf{A}=\begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}$

$|\mathbf{A}|=(\var{a11})*(\var{a22})-(\var{a12})*(\var{a21})=\simplify{{a11}*{a22}-{a12}*{a21}}$

The adjoint of the matrix is given by: $\mathbf{A^*}=\begin{pmatrix} d & -b\\ -c & a\\ \end{pmatrix}$

$\mathbf{A^*}=\begin{pmatrix} \var{a22} & \simplify{-{a12}}\\ \simplify{-{a21}} & \var{a11}\\ \end{pmatrix}$

We combine these results to get the inverse matrix: $\mathbf{A^{-1}}=\frac{1}{|\mathbf{A}|}\begin{pmatrix} d & -b\\ -c & a\\ \end{pmatrix}$

$A^{-1}=\begin{pmatrix} \var{b11} & \var{b12}\\ \var{b21} & \var{b22} \end{pmatrix}$

To solve the problem:

$\begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}\begin{pmatrix} x\\y\end{pmatrix}=\begin{pmatrix} \var{r}\\\var{s}\end{pmatrix}$

$\begin{pmatrix} x\\y\end{pmatrix}=\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \end{pmatrix}\begin{pmatrix} \var{r}\\\var{s}\end{pmatrix}$

$\begin{pmatrix} x\\y\end{pmatrix}=\begin{pmatrix}(\var{b11})*(\var{r})+(\var{b12})*(\var{s})\\(\var{b21})*(\var{r})+(\var{b22})*(\var{s})\end{pmatrix}$

$\begin{pmatrix} x\\y\end{pmatrix}=\begin{pmatrix}\simplify{{b11}*{r}+{b12}*{s}}\\\simplify{{b21}*{r}+{b22}*{s}}\end{pmatrix}$

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
Matrix entry
Matrix entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Matrix arithmetic by Frank Doheny in Matrices.
Mobius - ENG Test by Shaheen Charlwood in Shaheen's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 8 years ago

Frank Doheny 8 years ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Inverse of a 2x2 Matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 8 years ago

Frank Doheny 8 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`