Ex 4 Determinant of a 3 x 3 Matrix

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Created this as a copy of Ex 4 Determinant of a 3 x 3 Matrix.

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

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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	3
a12	integer	-4
a13	integer	4
a21	integer	-2
a22	integer	-2
a23	integer	-5
a31	integer	1
a32	integer	-1
a33	integer	-1
m1	integer	-3
m2	integer	7
m3	integer	4

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.

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Generated value: `matrix`

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

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Number entry
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Gap-fill

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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

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

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Violeta CIT 6 years, 6 months ago

Violeta CIT 6 years, 6 months ago

Error in variable testing condition

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Generated value: `matrix`

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Determinant of a $3 \times 3$ matrix

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Ex 4 Determinant of a 3 x 3 Matrix

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Comment

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Violeta CIT 6 years, 6 months ago

Violeta CIT 6 years, 6 months ago

Error in variable testing condition

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Generated value: matrix

Parts

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Determinant of a 3×33 \times 3 matrix

Generated value: `matrix`

Determinant of a $3 \times 3$ matrix