Matrix transformations (WBQ 1.30 randomised)

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Julia Goedecke

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From users who are members of Linear Algebra 1st year :

Iain Gunn	said	Ready to use	4 years, 6 months ago
Julia Goedecke	said	Needs to be tested	4 years, 6 months ago

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Iain Gunn 4 years, 6 months ago

Gave some feedback: Ready to use

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Julia Goedecke 4 years, 6 months ago

Published this.

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Julia Goedecke 4 years, 6 months ago

Gave some feedback: Needs to be tested

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Julia Goedecke 4 years, 6 months ago

Created this as a copy of Matrix transformations (same as WBQ 1.30).

Name	Status	Author	Last Modified
Matrix transformations (same as WBQ 1.30)	Ready to use	Julia Goedecke	25/08/2021 12:57
Matrix transformations (WBQ 1.30 randomised)	Ready to use	Julia Goedecke	25/08/2021 12:57
Demo variable number of gaps	Ready to use	Julia Goedecke	25/08/2021 12:57
Demo automatically generate latex for matrix/vector calculation	Ready to use	Julia Goedecke	25/08/2021 12:57
copy of Matrix transformations (WBQ 1.30 randomised)	Ready to use	Julia Goedecke	25/08/2021 12:57
Demo matrix of mathematical expressions	Ready to use	Julia Goedecke	25/08/2021 12:57

There are 19 other versions that do you not have access to.

Question statement

Let $A=\var{A}$ , $B=\var{B}$ , $u=\var{u}$ and $v=\var{v}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

A	matrix	matrix([-1,3],[-2,3])
B	matrix	matrix([0,0,0],[0,0,0])
u	vector	vector(0,3)
v	vector	vector(-1,-3)
m	integer	2
n	integer	2
rawunresolvedAu	list	List of 4 items
rawunresolvedAv	list	List of 4 items
rawunresolvedBu	list	List of 4 items
rawunresolvedBv	list	List of 4 items
unresolvedAu	string	\begin{pmatrix}(-1)\cdot0+3\cd
unresolvedAv	string	\begin{pmatrix}(-1)\cdot(-1)+3
unresolvedBu	string	\begin{pmatrix}0\cdot0+0\cdot3
unresolvedBv	string	\begin{pmatrix}0\cdot(-1)+0\cd
x	list	[ "x_1", "x_2" ]
rawAx	list	List of 4 items
halfrawAx	list	List of 2 items
latexAx	string	\begin{pmatrix}3x_2 - x_1\\3x_
Ax	list	[ -x_1 + 3x_2, -2x_1 + 3x_2 ]
xalt	list	[ "x1", "x2" ]
rawAxalt	list	List of 4 items
Axalt	list	[ -x1 + 3x2, -2x1 + 3x2 ]
halfrawx	list	[ "x_1\\\\", "x_2" ]
latexx	string	\begin{pmatrix}x_1\\x_2\end{pm

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
matrix(repeat(repeat(random(-3..3),n),m))

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: `matrix`

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

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Matrix entry
  Add
2. Gap Gap 1. Matrix entry
  Add
3. Gap Gap 2. Matrix entry
  Add
4. Gap Gap 3. Matrix entry
  Add
Part b) Gap-fill
1. Gap m Number entry
  Add
2. Gap n Number entry
  Add
Part c) Gap-fill

Gap-fill

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

Compute:

$Au =$ Gap 0.

$Av=$ Gap 1.

$Bu=$ Gap 2.

$Bv=$ Gap 3.

Advice

a) To calculate matrix times vector $Ax$ , we calculate this row by row: the first entry of the resulting vector is "row 1 of the matrix times the vector". In general:

$\begin{pmatrix} a_{11} & a_{12} &a_{13} \\ a_{21} & a_{22} & a_{23}\end{pmatrix} \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}= \begin{pmatrix} a_{11}x_1+a_{12}x_2 +a_{13}x_3\\ a_{21}x_1+a_{22}x_2 +a_{23}x_3\end{pmatrix}$

So the vector $x$ needs to have as many entries as the matrix has columns, and the resulting vector $Ax$ has as many entries as $A$ has rows.

$\var{A}\var{u}=\var{unresolvedAu}=\var{A*u}$

$\var{A}\var{v}=\var{unresolvedAv}=\var{A*v}$

$\var{B}\var{u}=\var{unresolvedBu}=\var{B*u}$

$\var{B}\var{v}=\var{unresolvedBv}=\var{B*v}$

b) As explained above, the matrix $A$ can take a vector $x$ with $\var{n}$ entries as input, and gives a vector $Ax$ with $\var{m}$ entries as output. This is a matrix transformation $T_A\colon { \mathbb{R}^{\var{n}} \to \mathbb{R}^{\var{m}}}$ , i.e. $n=\var{n}$ and $m=\var{m}$ .

c) As $n=\var{n}$ , we calculate $\var{A}\var{latexx} = \var{latexAx}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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

This question is not used in any exams.

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Matrix transformations (WBQ 1.30 randomised)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Iain Gunn 4 years, 6 months ago

Julia Goedecke 4 years, 6 months ago

Julia Goedecke 4 years, 6 months ago

Julia Goedecke 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `matrix`

Parts

Gap-fill

Loading...

Error

Matrix transformations (WBQ 1.30 randomised)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Iain Gunn 4 years, 6 months ago

Julia Goedecke 4 years, 6 months ago

Julia Goedecke 4 years, 6 months ago

Julia Goedecke 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: matrix

Parts

Gap-fill

Generated value: `matrix`