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Tamsin Smith 7 months, 1 week ago

Published this.

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Tamsin Smith 11 months, 2 weeks ago

Created this as a copy of Matrix Multiplication.

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

Matrix Multiplication

Given two matrices:

$\boldsymbol{A}=\begin{pmatrix} \var{a11}&\var{a12}&\var{a13}\\ \var{a21}&\var{a22}&\var{a23}\\ \end{pmatrix} ,\boldsymbol{B}=\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22}\\ \var{b31}&\var{b32}\\\end{pmatrix}$

Calculate the following matrix multiplications.

Give any introductory information the student needs.

			Name	Type	Generated Value

a11	integer	8
a12	integer	7
a21	integer	0
a22	integer	5
k	integer	8
a13	integer	10
a23	integer	14
b11	integer	8
b12	integer	6
b21	integer	5
b22	integer	11
b31	integer	0
b32	integer	7
ab11	integer	99
ab12	integer	195
ab21	integer	25
ab22	integer	153
ba11	integer	64
ba12	integer	86
ba13	integer	164
ba21	integer	40
ba22	integer	90
ba23	integer	204
ba31	integer	0
ba32	integer	35
ba33	integer	98

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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`

→ Used by:

a12
ab11
ab12
ba11
ba21
ba31

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Matrix entry
  Add
Part b) 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.

Calculate the product $\boldsymbol{AB}$

First set up the size of the answer matrix (choose the correct number of rows and columns in the boxes) and then input the entries:

$\boldsymbol{AB} =$ Unnamed gap

Advice

Remember multiplication of matrices is carried out by multiplying the rows of the first matrix by the columns of the second matrix

$\begin{aligned} \boldsymbol{A}\boldsymbol{B} &= \begin{pmatrix} \var{a11}&\var{a12}&\var{a13}\\ \var{a21}&\var{a22}&\var{a23} \end{pmatrix}\begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22} \\ \var{b31}&\var{b32}\end{pmatrix} \\ &= \begin{pmatrix}\var{a11}\times\var{b11}+\var{a12}\times\var{b21}+\var{a13}\times\var{b31}&\var{a11}\times\var{b12}+\var{a12}\times\var{b22}+\var{a13}\times\var{b32} \\ \var{a21}\times\var{b11}+\var{a22}\times\var{b21}+\var{a23}\times\var{b31}&\var{a21}\times\var{b12}+\var{a22}\times\var{b22}+\var{a23}\times\var{b32}\end{pmatrix} \\ &=\begin{pmatrix}\simplify{{a11}*{b11}+{a12}*{b21}+{a13}*{b31}}&\simplify{{a11}*{b12}+{a12}*{b22}+{a13}*{b32}}\\ \simplify{{a21}*{b11}+{a22}*{b21}+{a23}*{b31}}&\simplify{{a21}*{b12}+{a22}*{b22}+{a23}*{b32}}\end{pmatrix} \end{aligned}$

To evaluate $\boldsymbol{B}\boldsymbol{A}$ we swap their positions and this time multiply the rows of $\boldsymbol{B}$ by the columns of $\boldsymbol{A}$

$\begin{aligned} \boldsymbol{B}\boldsymbol{A} &= \begin{pmatrix} \var{b11}&\var{b12}\\ \var{b21}&\var{b22} \\ \var{b31}&\var{b32}\end{pmatrix} \begin{pmatrix} \var{a11}&\var{a12}&\var{a13}\\ \var{a21}&\var{a22}&\var{a23} \end{pmatrix} \\ &= \begin{pmatrix} \var{b11} \times \var{a11} + \var{b12} \times \var{a21} & \var{b11} \times \var{a12} + \var{b12} \times \var{a22} & \var{b11} \times \var{a13} + \var{b12} \times \var{a23} \\ \var{b21} \times \var{a11} + \var{b22} \times \var{a21} & \var{b21} \times \var{a12} + \var{b22} \times \var{a22} & \var{b21} \times \var{a13} + \var{b22} \times \var{a23} \\ \var{b31} \times \var{a11} + \var{b32} \times \var{a21} & \var{b31} \times \var{a12} + \var{b32} \times \var{a22} & \var{b31} \times \var{a13} + \var{b32} \times \var{a23} \\ \end{pmatrix} \\ &= \begin{pmatrix} \simplify{{b11}*{a11}+{b12}*{a21}} & \simplify{{b11} *{a12} + {b12} *{a22}} & \simplify{{b11}*{a13} + {b12}*{a23}} \\ \simplify{{b21}*{a11}+{b22}*{a21}} & \simplify{{b21}*{a12} + {b22}*{a22}} & \simplify{{b21}*{a13} + {b22}*{a23}} \\ \simplify{{b31}*{a11}+{b32}*{a21}} & \simplify{{b31}*{a12} + {b32}*{a22}} & \simplify{{b31}*{a13} + {b32}*{a23}} \\ \end{pmatrix} \\ \end{aligned}$

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Part	Test	Passed?
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Matrix entry
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This question is used in the following exam:

Matrix Multiplication by Fraser Buxton in Tamsin's workspace.

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Matrix Multiplication

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Contributors

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Tamsin Smith 7 months, 1 week ago

Tamsin Smith 11 months, 2 weeks ago

Matrix Multiplication

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Matrix Multiplication

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Tamsin Smith 7 months, 1 week ago

Tamsin Smith 11 months, 2 weeks ago

Matrix Multiplication

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`