Mark's copy of Inverse of a 2x2 Matrix

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Mark Hodds

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Mark Hodds 7 years, 7 months ago

Created this as a copy of Inverse of a 2x2 Matrix.

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	-5
a21	integer	11
a22	integer	-9
k	integer	2
det	integer	10
b11	rational	-9/10
b12	rational	1/2
b21	rational	-11/10
b22	rational	1/2
c	integer	10
r	integer	-15
s	integer	-13
r1	integer	7
s1	integer	10

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

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Generated value: `integer`

→ Used by:

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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.

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Part	Test	Passed?
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Matrix entry
Matrix entry		Hasn't run yet
Gap-fill
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Number entry
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Number entry
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This question is used in the following exam:

101MP 2019 - Matrices Week 4 by Mark Hodds in 101MP 2018.

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Taxonomy: mathcentre

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Mark Hodds 7 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Mark's copy of Inverse of a 2x2 Matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Mark Hodds 7 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`