1 Introduction to Matrices

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1 Introduction to Matrices

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Generated value: `integer`

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Gap-fill

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Generated value: `integer`

Parts

Gap-fill

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Generated value: integer

Parts

Gap-fill

Generated value: `integer`

Emer McGann 8 years, 3 months ago

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Emer McGann 8 years, 3 months ago

Error in variable testing condition

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Emer McGann 8 years, 3 months ago

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Emer McGann

○

Created this as a copy of Lois's copy of 1.1 Introduction to Matrices.

Name	Status	Author	Last Modified
Lois's copy of 1.1 Introduction to Matrices	draft	Lois Rollings	26/08/2016 11:41
Simon's copy of Lois's copy of 1.1 Introduction to Matrices	draft	Simon Vaughan	12/01/2017 10:05
1 Introduction to Matrices	draft	Emer McGann	25/11/2016 09:53
Laura's copy of 1 Introduction to Matrices	draft	Laura O'Brien	15/12/2016 14:33
Alex's copy of Simon's copy of Lois's copy of 1.1 Introduction to Matrices	draft	Alex Van den Hof	27/01/2017 10:55
Ch10 Q1	draft	Alex Van den Hof	20/02/2017 16:01
Matrices 1	draft	Mark Hodds	24/10/2018 09:06
Introduction to Matrices	draft	Marie Nicholson	04/02/2021 15:34
Blathnaid's copy of Matrices 1	draft	Blathnaid Sheridan	12/11/2018 13:22
Maria's copy of Introduction to Matrices	Needs to be tested	Maria Aneiros	23/05/2019 06:29
Maria's copy of Matrices 1	draft	Maria Aneiros	11/07/2019 07:44
Matrices 1	draft	Kevin Bohan	06/06/2019 11:02
L1 - Matrices intro and definitions	Ready to use	Timur Zaripov	17/06/2022 09:37

There are 11 other versions that do you not have access to.

Question statement

Matrices are rectangular arrays of numbers arranged in rows and columns. For example

$\begin{pmatrix} 1&2\\ 4&5\\ \end{pmatrix} , \begin{pmatrix} 0&-1\ &3\\2&4&-2 \end{pmatrix}$

The rows run across the matrices while the columns run down the matrices. Thus in the first matrix above the numbers $\begin{pmatrix}1&2\end{pmatrix}$ are in the first row while the numbers $\begin{pmatrix}4&5\end{pmatrix}$ are in the second row and similarly the numbers $\begin{pmatrix} 1\\ 4\\ \end{pmatrix}$ are in the first column while the numbers $\begin{pmatrix} 2\\ 5\\ \end{pmatrix}$ are in the second column.

A matrix with $\bf m$ rows and $\bf n$ columns is called a matrix of order $\bf m\times n$ or dimension $\bf m\times n$ (or an $\bf m\times n$ matrix for brevity).

When working with matrices the positions of the numbers in the arrays are as important as the actual values of the numbers. Given a matrix called $A$ the number in row $i$ and column $j$ is usually denoted $a_{ij}$ it is also sometimes called the $ij^{th}$ element of the matrix $A$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

n1	integer	2
m1	integer	2
A	matrix	matrix([-6,-2],[-1,-9])

			Name	Type	Generated Value

n2	integer	2
m2	integer	2
B	matrix	matrix([-9,-4],[-1,1])

			Name	Type	Generated Value

n3	integer	2
m3	integer	2
C	matrix	matrix([6,7],[1,3])

			Name	Type	Generated Value

			n4	integer	1
			m4	integer	1

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..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?

→ Used by:

"Part a)" → "Gap 0." - Minimum accepted value
"Part a)" → "Gap 0." - Maximum accepted value
"Part b)" - prompt
"Part b)" → "Gap 0." - Minimum accepted value
"Part b)" → "Gap 0." - Maximum accepted value

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
Part c) Choose one from a list
Part d) Match choices with answers

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

Example 1 -- Give the dimensions of the following matrices:

$A=\var{A}$ has dimensions Gap 0. $\times$ Gap 1.

$B=\var{B}$ is a Gap 2. $\times$ Gap 3. matrix

$C=\var{C}$ is of dimension Gap 4. $\times$ Gap 5.

Advice

a) Remember that the dimensions are $\rm \color{red}{rows} \times \color{blue}{columns}$ , so you need to count the number or rwos and columns in the matrix and wrtite them in that order.

b) Remember that the elements are in the form $A_{\rm \color{red}{ rows},\color{blue}{columns}}$ where $A$ is the matrix.

For example if we are looking for $a_{12}$ we look at the matrix $A= \begin{pmatrix} \var{a11} &\bf( \underline{\var{a12}}) \\ \var{a21} & \var{a22}\end{pmatrix}$ we want the the element on $\rm \color{red}{row ~ 1}$ and $\rm \color{blue}{column ~ 2}$ which in this case is $\bf \underline{\var{a12}}$

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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Match choices with answers
Match choices with answers		Hasn't run yet

This question is used in the following exam:

Matrices 1 by Emer McGann in Emer's workspace.

Definition of variable a11 is empty.

Definition of variable a12 is empty.

Definition of variable a21 is empty.

Definition of variable a22 is empty.