Matrix Multiplication 1 (2x2 matrices)

Error

There was an error loading the page.

Contributors

Marie Nicholson

History

○

Marie Nicholson 7 years ago

Created this as a copy of Question 2 MATH 6005 Assessment 1 Matrix Multiplication 1 (2x2 matrices).

Name	Status	Author	Last Modified
Matrix Multiplication 1	Ready to use	Bill Foster	01/06/2016 09:47
Eva's copy of Matrix Multiplication 1	Ready to use	Eva Szatmari	01/06/2016 09:47
Multiplicación de matrices 001	Ready to use	Jos Klenner	02/12/2020 15:42
Lois's copy of Matrix Multiplication 1	Ready to use	Lois Rollings	27/07/2016 10:50
Julie's copy of Matrix Multiplication 1	Ready to use	Julie Crowley	26/07/2016 12:53
Katie's copy of Matrix Multiplication 1	Ready to use	Katie Dexter	01/06/2016 09:47
Andrew's copy of Katie's copy of Matrix Multiplication 1	Ready to use	Andrew Iskauskas	01/06/2016 09:47
Andrew's copy of Andrew's copy of Katie's copy of Matrix Multiplication 1	Ready to use	Andrew Dunbar	01/06/2016 09:47
JUSTYNA's copy of Katie's copy of Matrix Multiplication 1	Ready to use	JUSTYNA NOWICZ	01/06/2016 09:47
Simon's copy of Lois's copy of Matrix Multiplication 1	draft	Simon Vaughan	09/11/2016 16:37
Alex's copy of Simon's copy of Lois's copy of Matrix Multiplication 1	draft	Alex Van den Hof	26/01/2017 14:17
Matrices: Multiplication 1	draft	Clare Lundon	04/03/2019 14:50
Matrix Multiplication	Ready to use	Frank Doheny	14/03/2018 21:05
Inverse of a 2x2 Matrix	Ready to use	Frank Doheny	14/03/2018 21:04
Andrew's copy of Matrices: Multiplication 1	draft	Andrew Dunbar	30/06/2017 22:04
Ex 2 Matrix Multiplication 1 (2x2 matrices)	draft	Violeta CIT	11/09/2017 10:47
Mark's copy of Inverse of a 2x2 Matrix	draft	Mark Hodds	07/09/2017 14:58
MATH6058 Matrix Multiplication 1 (2x2 matrices)	draft	Catherine Palmer	09/03/2023 19:52
Clodagh's copy of MATH6058 Matrix Multiplication 1 (2x2 matrices)	draft	Clodagh Carroll	26/09/2017 10:29
Question 2 MATH 6005 Assessment 1 Matrix Multiplication 1 (2x2 matrices)	Ready to use	Violeta CIT	04/10/2017 17:55
Question 2.1 MATH 6005 Assessment 1 Matrix Multiplication 2 (3x3 by 3x2 matrices)	Ready to use	Violeta CIT	17/06/2019 11:24
Ioannis's copy of Lois's copy of Matrix Multiplication 1	draft	Ioannis Lignos	28/10/2018 20:44
Matrices: Multiplication	draft	Clare Lundon	03/11/2017 16:44
Matrix Multiplication 1 (2x2 matrices)	draft	Marie Nicholson	04/02/2021 15:44
Matrix Multiplication (2x2)	draft	Marie Nicholson	04/02/2021 15:34
Joseph's copy of Matrix Multiplication 1	draft	Joseph Clarke	15/06/2018 14:25
Joseph's copy of Matrix Multiplication 1	draft	Antonia Wilmot-Smith	31/08/2018 12:23
Ex 2 Matrix Multiplication 1 (2x2 matrices)	Ready to use	Violeta CIT	16/09/2018 11:10
William's copy of Question 2.1 MATH 6005 Assessment 1 Matrix Multiplication 2 (3x3 by 3x2 matrices)	draft	William Lee	12/10/2018 15:03
Simon's copy of Matrix Multiplication 1	draft	Simon Thomas	01/04/2019 12:12
Quiz copy of Matrix Multiplication 1 (2x2 matrices)	draft	Marie Nicholson	07/05/2021 14:34
John's copy of Ex 2 Matrix Multiplication 1 (2x2 matrices)	draft	John Steele	13/05/2019 03:59
John's copy of Matrix Multiplication	draft	John Steele	13/05/2019 03:58
Josh's copy of Question 2.1 MATH 6005 Assessment 1 Matrix Multiplication 2 (3x3 by 3x2 matrices)	draft	Josh Lim	19/06/2019 16:35
Matrix Multiplication 2 (3x3 by 3x2 matrices)	draft	Xiaodan Leng	10/07/2019 21:35
Anthony's copy of Matrix Multiplication 1	draft	Anthony Brown	17/08/2019 10:43
Matrix Multiplication	draft	Thomas Waters	11/09/2019 21:34
Matrix Multiplication (2x3 by 3x2 matrices)	draft	Marie Nicholson	26/09/2019 12:29
L1 - Matrix Multiplication (2x3 by 3x2 matrices)	Ready to use	Timur Zaripov	17/06/2022 09:37
L1 - Matrix Multiplication (1x3 by 3x1 matrices)	Ready to use	Timur Zaripov	17/06/2022 09:37
Matrix Multiplication	draft	Shaheen Charlwood	19/02/2020 21:15
Matrix Multiplication	draft	Tamsin Smith	17/09/2024 13:11

There are 49 other versions that do you not have access to.

Question statement

Do the following matrix problems :
Let

$A=\begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix},\;\; B=\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \end{pmatrix},\;\;$
Calculate the following products of these matrices:

Give any introductory information the student needs.

			Name	Type	Generated Value

ba21	integer	8
a21	integer	-1
a22	integer	2
ba22	integer	2
cb21	integer	-12
b22	integer	-2
b21	integer	3
cb22	integer	-7
ac22	integer	1
ac21	integer	9
ab22	integer	-3
ab21	integer	9
b12	integer	-1
b11	integer	-3
c12	integer	1
c11	integer	1
c22	integer	1
a11	integer	2
cb11	integer	0
cb12	integer	-3
a12	integer	2
c21	integer	5
ba11	integer	-5
ba12	integer	-8
ab12	integer	-6
ab11	integer	0
ac12	integer	4
ac11	integer	12

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
b21*a11+b22*a21

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:

Advice

Parts

Gap-fill
1. Gap Matrix entry
  Add

Gap-fill

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

$AB = \begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \end{pmatrix} =$ Unnamed gap

Advice

a)

$\begin{eqnarray*} AB &=& \begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \simplify[]{{a11}{b11}+{a12}{b21}}&\simplify[]{{a11}{b12}+{a12}{b22}}\\ \simplify[]{{a21}{b11}+{a22}{b21}}&\simplify[]{{a21}{b12}+{a22}{b22}}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \var{ab11}&\var{ab12}\\ \var{ab21}&\var{ab22}\\ \end{pmatrix} \end{eqnarray*}$

b)

$\begin{eqnarray*} BA &=& \begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \end{pmatrix}\begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \simplify[]{{b11}{a11}+{b12}{a21}}&\simplify[]{{b11}{a12}+{b12}{a22}}\\ \simplify[]{{b21}{a11}+{b22}{a21}}&\simplify[]{{b21}{a12}+{b22}{a22}}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \var{ba11}&\var{ba12}\\ \var{ba21}&\var{ba22}\\ \end{pmatrix} \end{eqnarray*}$

c)

$\begin{eqnarray*} CB &=& \begin{pmatrix} \var{c11}&\var{c12}\\ \var{c21}&\var{c22}\\ \end{pmatrix}\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \simplify[]{{c11}{b11}+{c12}{b21}}&\simplify[]{{c11}{b12}+{c12}{b22}}\\ \simplify[]{{c21}{b11}+{c22}{b21}}&\simplify[]{{c21}{b12}+{a22}{b22}}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \var{cb11}&\var{cb12}\\ \var{cb21}&\var{cb22}\\ \end{pmatrix} \end{eqnarray*}$

d)

$\begin{eqnarray*} AC &=& \begin{pmatrix} \var{a11}&\var{a12}\\ \var{a21}&\var{a22}\\ \end{pmatrix}\begin{pmatrix} \var{c11}&\var{c12}\\ \var{c21}&\var{c22}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \simplify[]{{a11}{c11}+{a12}{c21}}&\simplify[]{{a11}{c12}+{a12}{c22}}\\ \simplify[]{{a21}{c11}+{a22}{c21}}&\simplify[]{{a21}{c12}+{a22}{c22}}\\ \end{pmatrix}\\ &=& \begin{pmatrix} \var{ac11}&\var{ac12}\\ \var{ac21}&\var{ac22}\\ \end{pmatrix} \end{eqnarray*}$

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
Matrix entry
Matrix entry		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Marie Nicholson 7 years ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

Loading...

Error

Matrix Multiplication 1 (2x2 matrices)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Marie Nicholson 7 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`