Calculating with vectors - fixed size - Numbas at mathcentre.ac.uk

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

Julia Goedecke

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Ready to use

4 years, 5 months ago

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Julia Goedecke 4 years, 5 months ago

Gave some feedback: Ready to use

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Julia Goedecke 4 years, 5 months ago

Published this.

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Julia Goedecke 4 years, 5 months ago

Created this as a copy of Calculating with vectors.

Name	Status	Author	Last Modified
Adding 2x2 matrices	Ready to use	Julia Goedecke	31/08/2021 10:06
Adding matrices of different sizes	Ready to use	Julia Goedecke	25/08/2021 12:57
Adding vectors	Ready to use	Julia Goedecke	25/08/2021 12:57
Adding and subtracting vectors	Ready to use	Julia Goedecke	25/08/2021 12:57
Calculating with vectors	Ready to use	Julia Goedecke	25/08/2021 12:57
Calculating with vectors - fixed size	Ready to use	Julia Goedecke	25/08/2021 12:57

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Question statement

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

Give any introductory information the student needs.

			Name	Type	Generated Value

rows	integer	4
v	vector	vector(4,-3,-3,2)
w	vector	vector(-3,4,0,4)
u	vector	vector(-2,-1,2,4)
sign1	integer	1
sign2	integer	1
lambda	integer	4
mu	integer	3
lambda1	integer	5
mu1	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
4

JME function reference

Description

size of the vectors

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

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0 Matrix entry
  1. Alt wrong brackets
  Add
Part b) Gap-fill
1. Gap Gap 0 Matrix entry
  1. Alt wrong brackets
  Add

Gap-fill

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

Calculate $\simplify{v + {lambda}*(u-{mu}w)}=$ Gap 0.

Advice

To multiply a vector by a scalar, we multiply each entry by that scalar. To add the resulting vectors, we add them entry by entry. Don't forget to resolve the brackets.

Part a)

$\simplify{v + {lambda}*(u-{mu}w)}=\begin{pmatrix}\simplify[]{{v[0]}+{lambda}*({u[0]}-{mu}*{w[0]})} \\ \simplify[]{{v[1]}+{lambda}*({u[1]}-{mu}*{w[1]})} \end{pmatrix} = \var{v+lambda*(u-mu*w)}$

$\simplify{v + {lambda}*(u-{mu}w)}=\begin{pmatrix}\simplify[]{{v[0]}+{lambda}*({u[0]}-{mu}*{w[0]})} \\ \simplify[]{{v[1]}+{lambda}*({u[1]}-{mu}*{w[1]})} \\\simplify[]{{v[2]}+{lambda}*({u[2]}-{mu}*{w[2]})} \end{pmatrix} = \var{v+lambda*(u-mu*w)}$

Part b)

$\simplify[]{{lambda1}*u +{mu}({mu1}v+{lambda}w)}=\begin{pmatrix}\simplify[]{{lambda1}{u[0]}+{mu}({mu1}{v[0]}+{lambda}*{w[0]})}\\ \simplify[]{{lambda1}{u[1]}+{mu}({mu1}{v[1]}+{lambda}*{w[1]})}\\ \simplify[]{{lambda1}{u[2]}+{mu}({mu1}{v[2]}+{lambda}*{w[2]})}\end{pmatrix}=\var{lambda1*u+mu*(mu1*v+lambda*w)}$

Give a worked solution to the whole question.

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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
Gap-fill
Gap-fill		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet

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Calculating with vectors - fixed size

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Julia Goedecke 4 years, 5 months ago

Julia Goedecke 4 years, 5 months ago

Julia Goedecke 4 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Calculating with vectors - fixed size

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Julia Goedecke 4 years, 5 months ago

Julia Goedecke 4 years, 5 months ago

Julia Goedecke 4 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`