Matrices: Basics 04

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Michael Proudman

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Needs to be tested

4 years, 9 months ago

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Michael Proudman 4 years, 9 months ago

Published this.

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Michael Proudman 4 years, 9 months ago

Gave some feedback: Needs to be tested

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Michael Proudman 4 years, 9 months ago

Created this as a copy of Matrices: Basics 01.

Name	Status	Author	Last Modified
Matrices: Basics 01	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Basics 02	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Basics 03	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Basics 04	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Add & Subtract 01	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Add & Subtract 03	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Add & Subtract 02	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Add & Subtract 04	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Scalar Multiple 01	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Scalar Multiple 02	Needs to be tested	Michael Proudman	07/12/2021 08:24
Matrices: Scalar Multiple 03	Needs to be tested	Michael Proudman	07/12/2021 08:24
Subtraction of Matrices	draft	Tamsin Smith	17/09/2024 13:13
Order of a Matrix	draft	Tamsin Smith	17/09/2024 12:41
Choosing an Element	draft	Tamsin Smith	17/09/2024 12:40
Finding the Transpose	draft	Tamsin Smith	17/09/2024 13:21
Scalar Multiple of a Matrix	draft	Tamsin Smith	17/09/2024 13:12
Addition and Subtraction with Scalar Multiples	draft	Tamsin Smith	17/09/2024 12:46
Addition of Matrices	draft	Tamsin Smith	16/09/2024 12:24

There are 9 other versions that do you not have access to.

Question statement

The transpose of a matrix $A$ is a matrix where the rows of $A$ become the columns of the new matrix and the columns of $A$ become its rows. For example:

$A= \left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6\ \end{array} \right)$ becomes $A^T= \left(\begin{array}{ccc} 1 & 4 \\ 2 & 5 \\ 3&6\ \end{array} \right)$

The resulting matrix is called the transposed matrix of $A$ and is denoted $A^T$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

n1	integer	1
m1	integer	2
A	matrix	matrix([0,-4])
TA	matrix	matrix([0],[-4])

			Name	Type	Generated Value

n2	integer	4
m2	integer	3
B	matrix	Matrix of size 4×3
TB	matrix	Matrix of size 3×4

			Name	Type	Generated Value

n3	integer	3
m3	integer	2
C	matrix	matrix([9,4],[-1,-2],[-9,7])
TC	matrix	matrix([9,-1,-9],[4,-2,7])

			Name	Type	Generated Value

n4	integer	1
m4	integer	1
D	matrix	matrix([-8])
TD	matrix	matrix([-8])

			Name	Type	Generated Value

n5	integer	2
m5	integer	1
EE	matrix	matrix([9],[8])
TE	matrix	matrix([9,8])

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..(m3-1) except m3)

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: `integer`

← Depends on:

→ Used by:

Parts

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
5. Gap Gap 4. Matrix entry
  Add

Gap-fill

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

Give the transpose of each matrix below.

You will have to define the dimension of the transposed matrix before you enter your answer.

$A=\var{A}$

$A^{T}=$ Gap 0.

$B=\var{B}$

$B^{T}=$ Gap 1.

$C=\var{C}$

$C^{T}=$ Gap 2.

$D=\var{D}$

$D^{T}=$ Gap 3.

$E=\var{EE}$

$E^{T}=$ Gap 4.

Advice

We are asked to work out the transpose of various matrices.

The transpose process results in rows becoming columns and columns becomimng rows.

It may help to imagine the matrix being "filpped" about its diagonal.

$A=\var{A}$ $A^{T}=\var{TA}$

$B=\var{B}$ $B^{T}=\var{TB}$

$C=\var{C}$ $C^{T}=\var{TC}$

$D=\var{D}$ $D^{T}=\var{TD}$

$E=\var{EE}$ $E^{T}=\var{TE}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Matrix entry
Matrix entry		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet
Matrix entry
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Matrix entry
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Matrix entry
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Taxonomy: mathcentre

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Checkpoint description

Michael Proudman 4 years, 9 months ago

Michael Proudman 4 years, 9 months ago

Michael Proudman 4 years, 9 months ago

The transpose of a matrix $A$ is a matrix where the rows of $A$ become the columns of the new matrix and the columns of $A$ become its rows. For example:

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Give the transpose of each matrix below.

We are asked to work out the transpose of various matrices.

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Error

Matrices: Basics 04

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Michael Proudman 4 years, 9 months ago

Michael Proudman 4 years, 9 months ago

Michael Proudman 4 years, 9 months ago

The transpose of a matrix AA is a matrix where the rows of AA become the columns of the new matrix and the columns of AA become its rows. For example:

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Give the transpose of each matrix below.

We are asked to work out the transpose of various matrices.

The transpose of a matrix $A$ is a matrix where the rows of $A$ become the columns of the new matrix and the columns of $A$ become its rows. For example:

Generated value: `integer`