Multiply 2x2 matrices

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

Name	Status	Author	Last Modified
Multiply 2x2 matrices	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
L1 - Matrix multiplication (2x2)	Ready to use	Timur Zaripov	17/06/2022 09:37
Musa's copy of L1 - Matrix multiplication (2x2)	draft	Musa Mammadov	01/08/2022 08:14
Musa's copy of Musa's copy of Matrices - 3	draft	Musa Mammadov	27/06/2023 01:43
Musa's copy of 3 L1 - Matrix multiplication (2x2)	draft	Musa Mammadov	27/06/2023 01:47

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Question statement

Let

$\begin{align} \mathbf{A} &= \var{a}, & \mathbf{B} &= \var{b}, & \mathbf{C} &= \var{c} \end{align}$

Calculate the following products of these matrices:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	matrix	matrix([1,3],[1,2])
b	matrix	matrix([-1,-3],[3,-3])
c	matrix	matrix([0,0],[3,0])

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
matrix([ [random(-2,1,2),random(1..4)], [random(-2..2),random(1..3)] ])

JME function reference

Description

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

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Generated value: `matrix`

matrix([1,3],[1,2])

→ Used by:

Statement
Advice
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer
"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer
"Part d)" - prompt
"Part d)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
1. Gap Matrix entry
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Part b) Gap-fill
1. Gap Matrix entry
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Part c) Gap-fill
1. Gap Matrix entry
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Part d) 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.

$\mathbf{AB} = \var{A}\var{B} =$ Unnamed gap

Advice

a)

$\begin{align} \mathbf{AB} &= \var{A}\var{B} \\ &= \begin{pmatrix} \simplify[]{ {a[0][0]}*{b[0][0]}+{a[0][1]}*{b[1][0]} } & \simplify[]{ {a[0][0]}*{b[0][1]} + {a[0][1]}*{b[1][1]} } \\ \simplify[]{ {a[1][0]}*{b[0][0]} + {a[1][1]}*{b[1][0]} } & \simplify[]{ {a[1][0]}*{b[0][1]} + {a[1][1]}*{b[1][1]} } \end{pmatrix} \\ &= \var{a*b} \end{align}$

b)

$\begin{align} \mathbf{BA} &= \var{B}\var{A} \\ &= \begin{pmatrix} \simplify[]{ {b[0][0]}*{a[0][0]}+{b[0][1]}*{a[1][0]} } & \simplify[]{ {b[0][0]}*{a[0][1]} + {b[0][1]}*{a[1][1]} } \\ \simplify[]{ {b[1][0]}*{a[0][0]} + {b[1][1]}*{a[1][0]} } & \simplify[]{ {b[1][0]}*{a[0][1]} + {b[1][1]}*{a[1][1]} } \end{pmatrix} \\ &= \var{b*a} \end{align}$

c)

$\begin{align} \mathbf{CB} &= \var{C}\var{B} \\ &= \begin{pmatrix} \simplify[]{ {c[0][0]}*{b[0][0]}+{c[0][1]}*{b[1][0]} } & \simplify[]{ {c[0][0]}*{b[0][1]} + {c[0][1]}*{b[1][1]} } \\ \simplify[]{ {c[1][0]}*{b[0][0]} + {c[1][1]}*{b[1][0]} } & \simplify[]{ {c[1][0]}*{b[0][1]} + {c[1][1]}*{b[1][1]} } \end{pmatrix} \\ &= \var{c*b} \end{align}$

d)

$\begin{align} \mathbf{AC} &= \var{A}\var{C} \\ &= \begin{pmatrix} \simplify[]{ {a[0][0]}*{c[0][0]}+{a[0][1]}*{c[1][0]} } & \simplify[]{ {a[0][0]}*{c[0][1]} + {a[0][1]}*{c[1][1]} } \\ \simplify[]{ {a[1][0]}*{c[0][0]} + {a[1][1]}*{c[1][0]} } & \simplify[]{ {a[1][0]}*{c[0][1]} + {a[1][1]}*{c[1][1]} } \end{pmatrix} \\ &= \var{a*c} \end{align}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Taxonomy: mathcentre

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Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: `matrix`

Parts

Gap-fill

a)

b)

c)

d)

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Multiply 2x2 matrices

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: matrix

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `matrix`