Linear combinations of 2 x 2 matrices

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Marie Nicholson

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Marie Nicholson 7 years, 1 month ago

Created this as a copy of Question 1 MATH6005 Assessment 1 Linear combinations of 2 x 2 matrices.

Name	Status	Author	Last Modified
Linear combinations of 2 x 2 matrices	Ready to use	Bill Foster	01/06/2016 09:47
Katie's copy of Linear combinations of 2 x 2 matrices	Ready to use	Katie Dexter	01/06/2016 09:47
Ex 1 Linear combinations of 2 x 2 matrices	draft	Violeta CIT	11/09/2017 10:47
MATH6058 Linear combinations of 2 x 2 matrices	draft	Catherine Palmer	21/10/2024 10:35
Question 1 MATH6005 Assessment 1 Linear combinations of 2 x 2 matrices	Ready to use	Violeta CIT	04/10/2017 17:55
Linear combinations of 2 x 2 matrices	draft	Marie Nicholson	06/02/2018 11:26
Linear combinations of 2 x 2 matrices	draft	Marie Nicholson	04/02/2021 15:34
Joseph's copy of Linear combinations of 2 x 2 matrices	draft	Antonia Wilmot-Smith	31/08/2018 12:23
Determinant of 2 x 2 matrices	Needs to be tested	Gemma Crowe	31/08/2018 16:37
Determinant of 3 x 3 matrices	Needs to be tested	Gemma Crowe	03/09/2018 11:55
Ex 1 Linear combinations of 2 x 2 matrices	Ready to use	Violeta CIT	01/10/2018 18:06
Simon's copy of Linear combinations of 2 x 2 matrices	draft	Simon Thomas	01/04/2019 12:09
Linear combinations of 2 dimensional vectors	draft	Marie Nicholson	04/02/2021 15:34
Linear combinations of 2 x 2 matrices	draft	Marie Nicholson	04/02/2021 15:34
Quiz copy of Linear combinations of 2 x 2 matrices	draft	Marie Nicholson	07/05/2021 14:34
John's copy of Determinant of 3 x 3 matrices	draft	John Steele	13/05/2019 03:58
Clodagh's copy of Ex 1 Linear combinations of 2 x 2 matrices	draft	Clodagh Carroll	25/09/2020 14:45
Ex 1 Linear combinations of 2 x 2 matrices draft 2	draft	Clodagh Carroll	25/09/2020 14:45
Add/Subtract 2 x 2 matrices	draft	Shaheen Charlwood	26/02/2020 12:29

There are 23 other versions that do you not have access to.

Question statement

Let
\[A=\simplify{{a}},\;\; B=\simplify{{b}},\;\; C=\simplify{{c}}\]
Calculate the following $2 \times 2$ matrices:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	matrix	matrix([5,-5],[5,-1])
q1	integer	-2
c	matrix	matrix([4,-2],[4,4])
b	matrix	matrix([-1,-3],[-5,-1])
r1	integer	5
q	integer	4
p	integer	6
p1	integer	2
apb	matrix	matrix([4,-8],[0,-2])
lcab	matrix	matrix([26,-42],[10,-10])
lcabc	matrix	matrix([32,-14],[40,20])

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
matrix(repeat(repeat(random(-5..5 except 0),2),2))

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([5,-5],[5,-1])

This variable doesn't seem to be used anywhere.

Parts

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

$\mathrm{A}+\mathrm{B} = $ Unnamed gap

Advice

a)

\[ \begin{eqnarray*} \simplify[std]{A+B} &=&\simplify[std]{{a}+{b}}\\ &=& \begin{pmatrix} \simplify[std]{{a[0][0]}+{b[0][0]}}& \simplify[std]{{a[0][1]}+{b[0][1]}}\\ \simplify[std]{{a[1][0]}+{b[1][0]}}&\simplify[std]{{a[1][1]}+{b[1][1]}} \end{pmatrix}\\ &=&\simplify{{apb}}\\ \end{eqnarray*} \]

b)

\[ \begin{eqnarray*} \simplify[std]{{p}A+{q}B} &=&\simplify[std]{{p}{a}+{q}{b}}\\ &=& \begin{pmatrix} \simplify[std]{{p}*{a[0][0]}+{q}*{b[0][0]}}& \simplify[std]{{p}*{a[0][1]}+{q}*{b[0][1]}}\\ \simplify[std]{{p}*{a[1][0]}+{q}*{b[1][0]}}&\simplify[std]{{p}*{a[1][1]}+{q}*{b[1][1]}} \end{pmatrix}\\ &=&\simplify{{lcab}}\\ \end{eqnarray*} \]

c)

\[ \begin{eqnarray*} \simplify[std]{{p1}A+{q1}B+{r1}C} &=&\simplify[std]{{p1}{a}+{q1}{b}+{r1}{c}}\\ &=& \begin{pmatrix} \simplify[std]{{p1}*{a[0][0]}+{q1}*{b[0][0]}+{r1}*{c[0][0]}}& \simplify[std]{{p1}*{a[0][1]}+{q1}*{b[0][1]}+{r1}*{c[0][1]}}\\ \simplify[std]{{p1}*{a[1][0]}+{q1}*{b[1][0]}+{r1}*{c[1][0]}}&\simplify[std]{{p1}*{a[1][1]}+{q1}*{b[1][1]}+{r1}*{c[1][1]}} \end{pmatrix}\\ &=&\simplify{{lcabc}}\\ \end{eqnarray*} \]

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Taxonomy: mathcentre

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Checkpoint description

Marie Nicholson 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `matrix`

Parts

Gap-fill

a)

b)

c)

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Linear combinations of 2 x 2 matrices

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Marie Nicholson 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: matrix

Parts

Gap-fill

a)

b)

c)

Generated value: `matrix`