Matrices: Scalar Multiple 01

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Michael Proudman

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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

Published this.

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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: Add & Subtract 03.

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

In general if $A$ is an $m \times n$ matrix with typical element $a_{ij}$ then the product of a number $k$ with $A$ is written $kA$ and has the corresponding elements $ka_{ij}$ .

If $A= \left( \begin{array}{ccc} a_{11} & a_{12} \\ a_{21} & a_{22} \\ a_{31} & a_{32} \end{array} \right)$ then $kA= \left( \begin{array}{ccc} k \times a_{11} & k \times a_{12} \\ k\times a_{21} &k\times a_{22} \\ k\times a_{31} &k\times a_{32} \end{array} \right)$

This operation is called scalar multiplication, but its result is not named "scalar product" to avoid confusion, since "scalar product" is often used as a synonym for the "dot product" or "inner product".

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	8
A2	matrix	Matrix of size 3×3

			Name	Type	Generated Value

n2	integer	2
m2	integer	4
B	matrix	Matrix of size 2×4
E2	number	-4
B2	matrix	Matrix of size 2×4

			Name	Type	Generated Value

n3	integer	3
m3	integer	5
C	matrix	Matrix of size 3×5
trC	number	4
C2	matrix	Matrix of size 3×5

			Name	Type	Generated Value

n4	integer	1
m4	integer	4
D	matrix	matrix([-1,7,4,-2])
D2	matrix	matrix([-8,1,5,0])

			Name	Type	Generated Value

n5	integer	1
m5	integer	4
EE	matrix	matrix([-4,8,8,1])
EE2	matrix	matrix([-9,-5,1,3])

			Name	Type	Generated Value

k1	integer	4
k2	integer	2
k3	integer	7
k4	integer	2
k5	integer	-2

			Name	Type	Generated Value

ad1	matrix	Matrix of size 3×3
ad2	matrix	Matrix of size 2×4
ad3	matrix	Matrix of size 3×5
ad4	matrix	matrix([-2,14,8,-4])
ad5	matrix	matrix([8,-16,-16,-2])

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:

"Unnamed part" → "Gap 0." - Number of rows

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
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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.

Carry out the scalar multiplication of the following matrices:

You will need to define the size of the matrix before entering your answer.

If $A=\var{A}$ then:

$\var{k1} A=$ Gap 0.

If $B=\var{B}$ then:

$\var{k2}B=$ Gap 1.

If $C=\var{C}$ then:

$\var{k3}C=$ Gap 2.

If $D=\var{D}$ then:

$\var{k4}D=$ Gap 3.

If $E=\var{EE}$ then:

$\var{k5}E=$ Gap 4.

Advice

We are asked to carry out scalar multiplications of the given matrices.

This is simply achieved by multiplying each element by the constant:

Using this technique results in:

If $A=\var{A}$ then: $\var{k1} A=\left( \begin{array}{ccc} \var{k1} \times \var{A[0][0]} & \var{k1} \times \var{A[0][1]}& \var{k1} \times \var{A[0][2]}\\ \var{k1} \times \var{A[1][0]} & \var{k1} \times \var{A[1][1]}& \var{k1} \times \var{A[1][2]}\\ \var{k1} \times \var{A[2][0]} & \var{k1} \times \var{A[2][1]} & \var{k1} \times \var{A[2][2]} \end{array} \right) = \var{ad1}$

Following the same process gives:

If $B=\var{B}$ then:

$\var{k2}B=\var{ad2}$

If $C=\var{C}$ then:

$\var{k3}C=\var{ad3}$

If $D=\var{D}$ then:

$\var{k4}D=\var{ad4}$

If $E=\var{EE}$ then:

$\var{k5}E=\var{ad5}$

Give a worked solution to the whole question.

URL

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

Matrices: Scalar Multiple (Instructional) by Michael Proudman in .Matrix Algebra.

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Checkpoint description

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

In general if $A$ is an $m \times n$ matrix with typical element $a_{ij}$ then the product of a number $k$ with $A$ is written $kA$ and has the corresponding elements $ka_{ij}$ .

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Carry out the scalar multiplication of the following matrices:

We are asked to carry out scalar multiplications of the given matrices.

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Error

Matrices: Scalar Multiple 01

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

In general if AA is an m×nm \times n matrix with typical element aija_{ij} then the product of a number kk with AA is written kAkA and has the corresponding elements kaijka_{ij} .

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Carry out the scalar multiplication of the following matrices:

We are asked to carry out scalar multiplications of the given matrices.

In general if $A$ is an $m \times n$ matrix with typical element $a_{ij}$ then the product of a number $k$ with $A$ is written $kA$ and has the corresponding elements $ka_{ij}$ .

Generated value: `integer`