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Tamsin Smith 6 months ago

Published this.

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Tamsin Smith 9 months, 2 weeks ago

Created this as a copy of Determinant and inverse of 2x2 matrices.

Name	Status	Author	Last Modified
Determinant and inverse of 2x2 matrices	Ready to use	Christian Lawson-Perfect	01/06/2016 11:03
Christoph's copy of Determinant and inverse of 2x2 matrices	Ready to use	Christoph Walti	01/06/2016 09:47
Determinant and inverse of 2x2 matrices	Ready to use	Michael Foreman	01/06/2016 09:47
Hina's copy of Determinant and inverse of 2x2 matrices	draft	Hina Ahmed	09/11/2016 13:32
Simon's copy of Hina's copy of Determinant and inverse of 2x2 matrices	draft	Simon Vaughan	09/11/2016 16:37
Alex's copy of Simon's copy of Hina's copy of Determinant and inverse of 2x2 matrices	draft	Alex Van den Hof	26/01/2017 14:17
Ch10 Q3	draft	Alex Van den Hof	20/02/2017 16:01
Ex 5 Determinant and Inverse of 2x2 matrices	Ready to use	Violeta CIT	21/09/2017 22:04
MATH6058 Determinant and Inverse of 2x2 matrices	draft	Catherine Palmer	25/09/2017 11:50
Question 4 MATH 6005 Assessment 1 Determinant and Inverse of 2x2 matrices	Ready to use	Violeta CIT	04/10/2017 17:56
Determinant and Inverse of 2x2 matrices	draft	Marie Nicholson	04/02/2021 15:34
Ex 5 Determinant and Inverse of 2x2 matrices	Ready to use	Violeta CIT	16/09/2018 11:11
Simon's copy of Determinant and inverse of 2x2 matrices	draft	Simon Thomas	01/04/2019 15:24
Determinant and Inverse of 2x2 matrices	draft	Xiaodan Leng	10/07/2019 23:31
Determinant and inverse of 2x2 matrices	draft	Shaheen Charlwood	19/02/2020 21:17
Inverse of a 2x2 matrix	draft	Tamsin Smith	17/09/2024 13:15

There are 24 other versions that do you not have access to.

Question statement

$2 \times 2$ Matrix Inverse

Find the inverse of the following matrix:

Give any introductory information the student needs.

			Name	Type	Generated Value

a11	integer	-3
a12	integer	-1
a21	integer	0
a22	integer	4
a	matrix	matrix([-3,-1],[0,4])

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-5..5)

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`

-3

→ Used by:

Parts

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.

Let:

$\boldsymbol{A} = \var{a}$

Calculate $\boldsymbol{A}^{-1}$

Input all the elements of the matrix as fractions or integers and not as decimals.

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

Advice

To find the inverse of a matrix we first need to find the determinant:

$\det \boldsymbol{A} = \var{a[0][0]} \times \var{a[1][1]} - \var{a[0][1]} \times \var{a[1][0]} = \var{det(a)}$

Since $\det \boldsymbol{A}\neq 0$ , we know that $\boldsymbol{A}$ is invertible with:

$\begin{aligned} \boldsymbol{A}^{-1} &= \frac{1}{\det \boldsymbol{A}} \begin{pmatrix} d & -b\\ -c& a \end{pmatrix} \\ &= \frac{1}{\var{det(a)}} \begin{pmatrix} \var{a[1][1]} & \var{-a[0][1]}\\ \var{-a[1][0]}& \var{a[0][0]} \end{pmatrix} \\ \end{aligned}$

Which gives us our inverse:

$\simplify[fractionnumbers]{matrix:A^(-1)={inverse(a)}}$

Give a worked solution to the whole question.

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

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Inverse of a 2x2 matrix

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Taxonomy: mathcentre

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Checkpoint description

Tamsin Smith 6 months ago

Tamsin Smith 9 months, 2 weeks ago

$2 \times 2$ Matrix Inverse

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

History

Comment

Checkpoint description

Tamsin Smith 6 months ago

Tamsin Smith 9 months, 2 weeks ago

2×22 \times 2 Matrix Inverse

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

$2 \times 2$ Matrix Inverse

Generated value: `integer`