Vectors - Introductory exercise (WB Q1.1 randomised)

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Julia Goedecke

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

andrew tonks	said	Ready to use	4 years, 7 months ago
Julia Goedecke	said	Needs to be tested	4 years, 8 months ago

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andrew tonks 4 years, 7 months ago

Gave some feedback: Ready to use

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Julia Goedecke 4 years, 8 months ago

Gave some feedback: Needs to be tested

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Julia Goedecke 4 years, 8 months ago

Published this.

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Julia Goedecke 4 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Vectors - Introductory exercise (WB Q1.1 randomised)	Ready to use	Julia Goedecke	25/08/2021 12:57
General linear combinations of standard basis vectors	Ready to use	Julia Goedecke	25/08/2021 12:57
Demo accept NA or any counter-example	Ready to use	Julia Goedecke	25/08/2021 12:57
copy of General linear combinations of standard basis vectors	Ready to use	Julia Goedecke	25/08/2021 12:57

There are 18 other versions that do you not have access to.

Question statement

Calculate the following:

Give any introductory information the student needs.

			Name	Type	Generated Value

v1	vector	vector(1,3)
v2	vector	vector(2,4)
w1	vector	vector(1.4142135624,pi)
w2	vector	vector(-0.7071067812,pi)
n	integer	2
b	integer	2
mu1	integer	4
mu2	integer	8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector((repeat(random(1..5),2)))

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: `vector`

vector(1,3)

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
  Add
Part b) Gap-fill
1. Gap Matrix entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
  Add

Gap-fill

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

$0\cdot \begin{pmatrix}x_1\\x_2\end{pmatrix}= \left( \begin{matrix}\phantom{.}\\\phantom{.}\\\phantom{.}\end{matrix}\right.$	Gap 0.	$\left.\begin{matrix}\phantom{.}\\\phantom{.}\\\phantom{.}\end{matrix}\right)$
	Gap 1.

Advice

We add vectors entry by entry, and we multiply a vector by a scalar by multiplying each entry.

Part a) Zero times any vector is the zero vector: $0\cdot \begin{pmatrix}x_1\\x_2\end{pmatrix}=\begin{pmatrix}0\\0\end{pmatrix}$ .

Part b)

$\var{v1}+\var{v2}=\begin{pmatrix}\simplify[]{{v1[0]}+{v2[0]}} \\ \simplify[]{{v1[1]}+{v2[1]}} \end{pmatrix} = \var{v1+v2}$

Part c)

$\var{mu1}\begin{pmatrix}\sqrt{\var{n}}\\\var{w1[1]}\end{pmatrix}+\var{mu2}\begin{pmatrix}-\frac{\sqrt{\var{n}}}{\var{b}}\\\var{w2[1]}\end{pmatrix}=\begin{pmatrix}\var{mu1}\sqrt{\var{n}}-\var{mu2}\frac{\sqrt{\var{n}}}{\var{b}}\\\var{mu1}\var{w1[1]}+\var{mu2}\var{w2[1]}\end{pmatrix} = \var{mu1*w1+mu2*w2}$

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Mathematical expression
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Gap-fill
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Matrix entry
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This question is used in the following exams:

Vectors Introduction by Julia Goedecke in Linear Algebra 1st year.
Week 4 Vectors intro by Timur Zaripov in XE420.
Vectors Introduction by Zeke Ahern in MXB100 quizzes.
Quiz G by Zeke Ahern in MXB100 quizzes.
Quiz G by Zeke Ahern in Zeke's workspace.
NCDCS Test UNIT 1 Introduction to Matrices & Vectors by Terry Young in NCDCS Unit 0 Course Intro.
XE420-21 - W4 - Introduction to Vectors by Timur Zaripov in XE420.
XE420-22 - W04 - Introduction to Vectors by Timur Zaripov in XE420.
NCM4 FE-F2022 UNIT 8 All by Terry Young in NCM4 FINAL EXAM Fall 2022.
XE420-24 - W04 - Introduction to Vectors by Timur Zaripov in XE420.
Linear algebra by Farai Nechikwira in Farai's workspace.

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Vectors - Introductory exercise (WB Q1.1 randomised)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Comment

Checkpoint description

andrew tonks 4 years, 7 months ago

Julia Goedecke 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

Loading...

Error

Vectors - Introductory exercise (WB Q1.1 randomised)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

andrew tonks 4 years, 7 months ago

Julia Goedecke 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Julia Goedecke 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`