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

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Harry Flynn

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Harry Flynn 7 years 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	5
a11	integer	1
a12	integer	5
a13	integer	20
a21	integer	5
a22	integer	24
a23	number	95
a31	integer	10
a32	integer	10
a33	integer	1
b	integer	5
b24	integer	-945
b25	integer	199
c	integer	2
c1	integer	3
c2	integer	1
c3	integer	1
f1	integer	1
f2	integer	1
f3	integer	1
g1	integer	1
g2	integer	1
g3	integer	1
s	integer	1

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Name

Data type

Value

xxxxxxxxxx
 
random(2..6)

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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
"Part b)" → "Gap 2." - Maximum accepted value
"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
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Part b) Gap-fill
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Part c) Gap-fill
1. Gap Gap 0. Number entry
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11. Gap Gap 10. Number entry
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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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Harry's copy of Invert a 3x3 matrix using row operations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 7 years ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Part 1.

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Error

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

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 7 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Part 1.

Generated value: `integer`