Matrices: Basics 03

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Michael Proudman

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Needs to be tested

4 years, 10 months ago

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Michael Proudman 4 years, 10 months ago

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Michael Proudman 4 years, 10 months ago

Gave some feedback: Needs to be tested

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Michael Proudman 4 years, 10 months ago

Created this as a copy of Matrices: Basics 02.

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

Square Matrices

When the number of rows is the same as the number of colums i.e. $m=n$ , the matrix is said to be square and of order $n$ (or $m$ since they are the same).

In an $n \times n$ square matrix $A$ , the leading diagonal (or principal diagonal) is the top-left to bottom right collection of elements $a_{11}, a_{22}, a_{33}, . . . ,a_{nn}$ .

The sum of the elements in the leading diagonal of $A$ is called the trace of the matrix and we write it as $tr(A)$ .

If $A= \left( \begin{array}{ccc} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n}\\ \vdots & \vdots & \vdots & \vdots\\ a_{n1} & a_{n2} & ... & a_{nn} \end{array} \right)$ then $tr(A)= a_{11}+a_{22}+...+a_{nn}$

Give any introductory information the student needs.

			Name	Type	Generated Value

n1	integer	3
m1	integer	3
A	matrix	Matrix of size 3×3
e1	number	3
trA	number	5

			Name	Type	Generated Value

n2	integer	2
m2	integer	2
B	matrix	matrix([4,-6],[5,5])
E2	number	5
trB	number	9

			Name	Type	Generated Value

n3	integer	5
m3	integer	5
C	matrix	Matrix of size 5×5
E3	number	-3
E4	number	4
trC	number	15

			Name	Type	Generated Value

n4	integer	4
m4	integer	4
D	matrix	Matrix of size 4×4
trD	number	9

			Name	Type	Generated Value

n5	integer	3
m5	integer	3
EE	matrix	Matrix of size 3×3
trE	number	-8

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

(a number)

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:

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Ask the student a question, and give any hints about how they should answer this part.

Calculate the trace of the following matrices:

$A=\var{A}$

$tr(A)=$ Gap 0.

$B=\var{B}$

$tr(B)=$ Gap 1.

$C=\var{C}$

$tr(C)=$ Gap 2.

$D=\var{D}$

$tr(D)=$ Gap 3.

$E=\var{EE}$

$tr(E)=$ Gap 4.

Advice

We are presented with random matrices and asked to calculate the trace of each one.

Remembering that, for a square matrix, the trace is the sum of the elements in the leading diagonal.

Begin at the top left element and work down to the bottom right element, adding as you go.

$A=\var{A}$

$tr(A)=\var{A[0][0]}+\var{A[1][1]} +\var{A[2][2]}=\var{trA}$

$B=\var{B}$

$tr(B)=\var{B[0][0]}+\var{B[1][1]}=\var{trB}$

$C=\var{C}$

$tr(C)=\var{C[0][0]}+\var{C[1][1]} +\var{C[2][2]}+\var{C[3][3]} +\var{C[4][4]}=\var{trC}$

$D=\var{D}$

$tr(D)=\var{D[0][0]}+\var{D[1][1]} +\var{D[2][2]}+\var{D[3][3]}=\var{trD}$

$E=\var{EE}$

$tr(E)=\var{EE[0][0]}+\var{EE[1][1]} +\var{EE[2][2]}=\var{trE}$

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?
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This question is used in the following exams:

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Taxonomy: mathcentre

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Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

Square Matrices

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Calculate the trace of the following matrices:

We are presented with random matrices and asked to calculate the trace of each one.

Loading...

Error

Matrices: Basics 03

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

Square Matrices

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Calculate the trace of the following matrices:

We are presented with random matrices and asked to calculate the trace of each one.

Generated value: `integer`