Hollie's copy of Invert a 3x3 matrix using row operations

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Hollie Tarr

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Chris Saker was given access to the Hollie's copy of Invert a 3x3 matrix using row operations 8 years, 3 months ago

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Hollie Tarr 8 years, 3 months ago

Created this as a copy of Invert a 3x3 matrix using row operations.

Name	Status	Author	Last Modified
Invert a 3x3 matrix using row operations	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Hollie's copy of Invert a 3x3 matrix using row operations	draft	Hollie Tarr	01/12/2016 12:33
Hollie's copy of Invert a 3x3 matrix using row operations	draft	Hollie Tarr	22/02/2017 14:22
Harry's copy of Invert a 3x3 matrix using row operations	draft	Harry Flynn	09/03/2018 14:46
Maria's copy of Invert a 3x3 matrix using row operations	draft	Maria Aneiros	23/05/2019 07:00
Simon's copy of Invert a 3x3 matrix using row operations	draft	Simon Thomas	12/06/2019 13:51

There are 18 other versions that do you not have access to.

Question statement

Find the inverse of the following matrix:

$A = \left(\begin{array}{rrr} \var{a11} & \var{a12} & \var{a13}\\ \var{a21} & \var{a22} & \var{a23}\\ \var{a31} & \var{a32} & \var{a33}\\ \end{array}\right)$

Form the $3 \times 6$ augmented matrix $B$ by placing $I_3$ to the right of $A$ as below:

$B = \left(\begin{array}{rrr|ccc} \var{a11} & \var{a12} & \var{a13} &\var{1}&\var{0}&\var{0}\\ \var{a21} & \var{a22} & \var{a23}&\var{0}&\var{1}&\var{0}\\ \var{a31} & \var{a32} & \var{a33}&\var{0}&\var{0}&\var{1}\\ \end{array}\right)$

In subsequent parts work with this matrix using row operations and introduce the identity matrix on the left hand side with the inverse of A eventually appearing on the right hand side.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
a11	integer	1
a12	integer	4
a13	integer	-8
a21	integer	-3
a22	integer	-11
a23	number	21
a31	integer	-3
a32	integer	-4
a33	integer	1
b	integer	4
b24	integer	-60
b25	integer	-23
c	integer	1
c1	integer	2
c2	integer	3
c3	integer	2
f1	integer	1
f2	integer	-1
f3	integer	-1
g1	integer	1
g2	integer	1
g3	integer	-1
s	integer	-1

Automatically regenerate variables?

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Data type

Value

xxxxxxxxxx
 
random(2..6)

JME function reference

Description

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Generated value: `integer`

→ Used by:

"Part a)" → "Gap 3." - Minimum accepted value
"Part a)" → "Gap 3." - Maximum accepted value
"Part a)" → "Gap 4." - Minimum accepted value
"Part a)" → "Gap 4." - Maximum accepted value
"Part b)" → "Gap 0." - Minimum accepted value
"Part b)" → "Gap 0." - Maximum accepted value
"Part b)" → "Gap 1." - Minimum accepted value
"Part b)" → "Gap 1." - Maximum accepted value
"Part b)" → "Gap 2." - Minimum accepted value
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"Part b)" → "Gap 5." - Minimum accepted value
"Part b)" → "Gap 5." - Maximum accepted value
"Part c)" → "Gap 2." - Minimum accepted value
"Part c)" → "Gap 2." - Maximum accepted value
"Part c)" → "Gap 3." - Minimum accepted value
"Part c)" → "Gap 3." - Maximum accepted value
"Part c)" → "Gap 8." - Minimum accepted value
"Part c)" → "Gap 8." - Maximum accepted value

Parts

Part a) Gap-fill
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Gap-fill

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

Part 1.

Introduce zeros in the first column below the first entry by adding suitable multiples of the first row to rows 2 and 3.

Input all numbers as fractions or integers and not as decimals.

$\left( \begin{matrix} \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \end{matrix} \right.$	$\var{a11}$	$\var{a12}$	$\var{a13}$	$1$	$0$	$0$	$\left) \begin{matrix} \phantom{.} \\ \phantom{.}\\ \phantom{.}\\ \phantom{.}\\ \end{matrix} \right.$
	$0$	Gap 0.	Gap 1.	Gap 2.	$1$	$0$
	$0$	Gap 3.	Gap 4.	Gap 5.	$0$	$1$

Now, if necessary, multiply the second row by a suitable number so that the second entry in the second row is 1.

Advice

All of the working is now shown

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

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This question is used in the following exams:

Row reductions by Hollie Tarr in MA114 - Old.
Gauss Jordan and Row Reduction by Hollie Tarr in MA114 - Old.

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Hollie's copy of Invert a 3x3 matrix using row operations

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Chris Saker was given access to the Hollie's copy of Invert a 3x3 matrix using row operations 8 years, 3 months ago

Hollie Tarr 8 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Part 1.

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Error

Hollie's copy of Invert a 3x3 matrix using row operations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Chris Saker was given access to the Hollie's copy of Invert a 3x3 matrix using row operations 8 years, 3 months ago

Hollie Tarr 8 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Part 1.

Generated value: `integer`