Find the Determinant of a 3 x 3 Matrix

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

Feedback

From users who are not members of Content created by Newcastle University :

Terry Young

said

Ready to use

2 years, 11 months ago

History

○

Terry Young 2 years, 11 months ago

Gave some feedback: Ready to use

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Find the Determinant of a 3 x 3 Matrix	Ready to use	Newcastle University Mathematics and Statistics	26/04/2022 19:09
Ex 4 Determinant of a 3 x 3 Matrix	draft	Violeta CIT	11/09/2017 10:49
Question 3 MATH6005 Assessment 1 Determinant of a 3 x 3 Matrix	Ready to use	Violeta CIT	04/10/2017 17:56
Stephen's copy of Question 3 MATH6005 Assessment 1 Determinant of a 3 x 3 Matrix	Ready to use	Thomas Winyard	27/07/2021 12:11
Harry's copy of Find the Determinant of a 3 x 3 Matrix	draft	Harry Flynn	09/03/2018 14:47
Ex 4 Determinant of a 3 x 3 Matrix	Ready to use	Violeta CIT	16/09/2018 11:11
Maria's copy of Find the Determinant of a 3 x 3 Matrix	draft	Maria Aneiros	07/02/2020 05:51
Determinant of a 3 x 3 Matrix	draft	Xiaodan Leng	10/07/2019 23:31
Determinant of a 3 x 3 Matrix	draft	Xiaodan Leng	11/07/2019 01:10
Matt's copy of Ex 4 Determinant of a 3 x 3 Matrix	draft	Matt Tranter	16/09/2019 10:55
W1b - Find the Determinant of a 3x3 Matrix	Ready to use	Timur Zaripov	17/06/2022 09:37

There are 24 other versions that do you not have access to.

Question statement

Consider the $3 \times 3$ matrix,

$\begin{align} \mathrm{A} &= \var{a} \end{align}$

Give any introductory information the student needs.

			Name	Type	Generated Value

matrix

Matrix of size 3×3

			Name	Type	Generated Value

a11	integer	-1
a12	integer	1
a13	integer	2
a21	integer	-5
a22	integer	-4
a23	integer	1
a31	integer	-3
a32	integer	-2
a33	integer	-2
m1	integer	10
m2	integer	13
m3	integer	-2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
matrix([ [a11,a12,a13],[a21,a22,a23],[a31,a32,a33] ])

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: `matrix`

matrix([-1,1,2],[-5,-4,1],[-3,-2,-2])

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Calculate the determinant of the matrix.

$\operatorname{det}\left( \mathrm{A}\right) =$ Unnamed gap

Advice

Determinant of a $3 \times 3$ matrix

The determinant of a matrix $\mathrm{M} = \begin{pmatrix} a&b&c \\ d&e&f \\ g&h&i \end{pmatrix}$ can be calculated by using cofactor expansion. Expanding along the first row,

$\det\left(\mathrm{M}\right) = a \cdot \det \begin{pmatrix} e&f \\ h&i \end{pmatrix}- b \cdot \det \begin{pmatrix} d&f \\ g&i \end{pmatrix} + c \cdot \det \begin{pmatrix} d&e \\ g&h \end{pmatrix}$

Thus for our example we have:

$\begin{align} \det \begin{pmatrix} e&f \\ h&i \end{pmatrix} &= \simplify[]{({a22}*{a33})-({a23}*{a32}) = {m1}} \\ \det \begin{pmatrix} d&f \\ g&i \end{pmatrix} &= \simplify[]{({a21}*{a33})-({a23}*{a31}) = {m2}} \\ \det \begin{pmatrix} d&e \\ g&h \end{pmatrix} &=\simplify[]{ ({a21}*{a32})-({a22}*{a31}) ={m3}} \end{align}$

and so

$\begin{align} \det\left(\mathrm{A}\right) = (\simplify[]{{a11}*{m1}})-(\simplify[]{{a12}*{m2}})+(\simplify[]{{a13}*{m3}}) = \simplify[]{{det(a)}} \end{align}$

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

This question is used in the following exams:

Matrices by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
MATH6005 Matrices by Julie Crowley in MATH6005 Engineering Mathematics 101.
MATH6005 Matrices Violeta Copy by Violeta CIT in MATH6005 Engineering Mathematics 101.
Maria's copy of Matrices by Maria Aneiros in Maria's workspace.
Ann's copy of Matrices by Ann Smith in Ann's workspace.
Ann's copy of Matrices by Ann Smith in Ann's workspace.
Matrices by Jeremie Wenger in Jeremie's workspace.
Mark's copy of Matrices by Mark Patterson in Mark's workspace.
Riya's copy of Matrices by Riya Sharma in Riya's workspace.
Matrices Exam from Newcastle by Samuel Frost in Matrices @ The College.
REVIEW Matrices and Determinants by Terry Young in NC Math 4.
Questions on inverse, determinant and Gauss elimination by Kuldeep Singh in Kuldeep's workspace.
exam matrices eerste versie by abc temp in abc's workspace.
Mid Unit Revision by Mike Phipps in Maths for STEM.
Algebra - NEWCASTLE questions by Morgiane Richard in Mathematics for Geosciences.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Terry Young 2 years, 11 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `matrix`

Parts

Gap-fill

Determinant of a $3 \times 3$ matrix

Loading...

Error

Find the Determinant of a 3 x 3 Matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Terry Young 2 years, 11 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: matrix

Parts

Gap-fill

Determinant of a 3×33 \times 3 matrix

Generated value: `matrix`

Determinant of a $3 \times 3$ matrix