Inverse of 2x2 matrix

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Peter Johnston 6 years, 1 month ago

Created this as a copy of Solve simultaneous equations by finding inverse matrix.

Name	Status	Author	Last Modified
Solve simultaneous equations by finding inverse matrix,	Ready to use	Newcastle University Mathematics and Statistics	21/12/2022 13:36
Blathnaid's copy of Solve simultaneous equations by finding inverse matrix,	draft	Blathnaid Sheridan	12/11/2018 13:23
Solve simultaneous equations by finding inverse matrix	draft	Morteza Shahpari	20/11/2018 05:28
Morteza's copy of Solve simultaneous equations by Crammer's method	draft	Morteza Shahpari	23/11/2018 06:03
Simon's copy of Solve simultaneous equations by finding inverse matrix,	draft	Simon Thomas	01/04/2019 15:36
Inverse of 2x2 matrix	draft	Peter Johnston	16/04/2019 03:48
sean's copy of Simon's copy of Solve simultaneous equations by finding inverse matrix,	draft	sean hunte	07/05/2019 20:25
Maria's copy of Solve simultaneous equations by finding inverse matrix,	draft	Maria Aneiros	23/05/2019 07:00
W1b - Solve simultaneous equations by finding inverse matrix	Ready to use	Timur Zaripov	17/06/2022 09:37
Alexander's copy of Solve simultaneous equations by finding inverse matrix,	draft	Alexander Corner	22/10/2024 10:09
M2	Ready to use	Shaheen Charlwood	16/05/2022 14:24

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Question statement

Consider the 2x2 matrix $\mathbf{A} = \var{ma}$ .

Input all numbers as fractions or integers and not as decimals.

Give any introductory information the student needs.

			Name	Type	Generated Value

ma	matrix	matrix([7,4],[1,-5])
a00	integer	7
a01	integer	4
a10	integer	1
a11	integer	-5
mb	matrix	matrix([-9],[-3])
ma_inverse	matrix	Matrix of size 2×2
x	number	-1.4615384615
y	number	0.3076923077

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
matrix([
    [a00,a01],
    [a10,a11]
])

JME function reference

Description

Matrix A. a10 is picked so it's non-singular, and a11 is never $\pm a01$ .

No entry is 0.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `matrix`

matrix([7,4],[1,-5])

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This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Matrix entry
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Gap-fill

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

Find the inverse of $\mathbf{A}$ .

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

Advice

The inverse of the 2x2 matrix $\mathbf{A} = \left ( \begin{matrix}a&b\\c&d \end{matrix} \right )$ is given by

$\mathbf{A}^{-1} = \frac{1}{\det(\mathbf{A})} \left ( \begin{matrix} d&-b\\-c&a \end{matrix} \right )$ .

Hence, as $\mathrm{det}(\mathbf{A}) = \simplify[]{ {ma[0][0]}*{ma[1][1]} - {ma[0][1]}*{ma[1][0]}} = \var{det(ma)} \neq 0$ , so $\mathbf{A}$ is invertible. Therefore

$\mathbf{A}^{-1} = \simplify[fractionnumbers]{{ma_inverse}}$

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

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Taxonomy: mathcentre

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Peter Johnston 6 years, 1 month ago

Error in variable testing condition

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Generated value: `matrix`

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Inverse of 2x2 matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Peter Johnston 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: matrix

Parts

Gap-fill

Generated value: `matrix`