Ugur's copy of Determine if vectors form a spanning set

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Created this as a copy of Determine if vectors form a spanning set.

Name	Status	Author	Last Modified
Determine if vectors form a spanning set	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Simon's copy of Determine if vectors form a spanning set	draft	Simon Thomas	12/06/2019 15:02
Ugur's copy of Determine if vectors form a spanning set	Ready to use	Ugur Efem	13/10/2024 20:15

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Question statement

Consider the following $5$ vectors in $\mathbb{R^4}$ .

$\begin{align} \textbf{v}_1&=\var{rowvector(v1)}\\ \textbf{v}_2&=\var{rowvector(v2)}\\ \textbf{v}_3&=\var{rowvector(v3)}\\ \textbf{v}_4&=\var{rowvector(v4)}\\ \textbf{v}_5&=\var{rowvector(v5)}\end{align}$

Give any introductory information the student needs.

			Name	Type	Generated Value

f1	integer	-1
f2	integer	0
f3	integer	0
f4	integer	0
another	string	There is one other simple rela
eg	string	This is one of the relations.
al	integer	-1
ga1	integer	0
are	string	are
ga	integer	1
ep	integer	0
es	string	s
contains	string	does not contain
be1	integer	1
nt	string	not
be	integer	0
v1	list	[ -1, -1, 1, 0 ]
v2	list	[ 1, 1, -3, 4 ]
v3	list	[ 1, 1, -1, 0 ]
v4	list	[ 2, 2, -4, 4 ]
v5	list	[ -3, 3, -1, 0 ]
b	integer	2
c5	integer	1
al1	integer	-1
a	integer	2
c	integer	1
p1	list	[ 1, 1, -1, 0 ]
thismany	integer	2
mm	list	[ 0, 1 ]
t0	integer	3
q	list	[ 1, 1, -1, 0 ]
p2	list	[ 2, 2, -4, 4 ]
r	list	[ -2, 4, -2, 0 ]
u	integer	4
t	list	[ 0, 0, 0, 0 ]
v	list	[ -1, 1, 0, 1 ]
y	list	[ 1, 1, -3, 4 ]
x	list	[ -1, -1, 1, 0 ]
z	list	[ -3, 3, -1, 0 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
if(u<9,al,0)

JME function reference

Description

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

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Generated value: `integer`

-1

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

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1. Is $\{\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4,\;\textbf{v}_5\}$ a linearly independent set of vectors? Gap 0.

2. Do the above vectors form a spanning set of $\mathbb{R}^4$ ? Gap 1.

3. Does the set $\{\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4,\;\textbf{v}_5\}$ contain a linearly independent subset which forms a basis of $\mathbb{R}^4$ ? Gap 2.

Advice

1. Not linearly independent as any set of more than $4$ vectors in $\mathbb{R^4}$ is linearly dependent.

2. They are spanning if any vector in $\mathbb{R^4}$ can be written as a linear combination of these vectors. This means that there must be $4$ linearly independent vectors in the list. If there are not then it is not spanning.

3. This set {contains} a linearly independent subset of $4$ vectors as it is {nt} spanning.

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This question is used in the following exam:

Linear Algebra 1 by Ugur Efem in Ugur's workspace.

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Ugur's copy of Determine if vectors form a spanning set

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Taxonomy: mathcentre

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Ugur Efem 5 months, 3 weeks ago

Ugur Efem 5 months, 3 weeks ago

Ugur Efem 5 months, 3 weeks ago

Error in variable testing condition

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Generated value: `integer`

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Ugur's copy of Determine if vectors form a spanning set

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ugur Efem 5 months, 3 weeks ago

Ugur Efem 5 months, 3 weeks ago

Ugur Efem 5 months, 3 weeks ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`