Simon's copy of Are given matrices in (reduced) row echelon form?

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Simon Thomas 5 years, 9 months ago

Created this as a copy of Are given matrices in (reduced) row echelon form?.

Name	Status	Author	Last Modified
Are given matrices in (reduced) row echelon form?	draft	Newcastle University Mathematics and Statistics	12/10/2021 20:12
Are given matrices in (reduced) row echelon form?	draft	Timothy Gould	25/02/2018 06:02
Are given matrices in (reduced) row echelon form?	draft	Marie Nicholson	22/04/2021 14:00
Maria's copy of Are given matrices in (reduced) row echelon form?	draft	Maria Aneiros	23/05/2019 06:31
Simon's copy of Are given matrices in (reduced) row echelon form?	draft	Simon Thomas	12/06/2019 15:21

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Question statement

Echelon Forms

For each of the following matrices choose which are:

a) In row echelon form but not in reduced row echelon form.

b) In reduced row echelon form.

c) Neither a) nor b).

Give any introductory information the student needs.

			Name	Type	Generated Value

b23	integer	1
d	matrix	Matrix of size 4×6
g26	integer	0
g24	integer	0
g25	integer	5
g22	integer	0
g23	integer	1
u1	integer	3
u2	integer	0
g45	integer	0
g46	integer	1
c13	integer	0
c12	integer	1
g33	integer	0
mf1	number	0.6
mf2	number	0
mb1	integer	0
mb2	number	0.6
mb3	number	0
a	matrix	Matrix of size 3×4
c	matrix	Matrix of size 4×5
b	matrix	Matrix of size 3×4
g35	integer	-1
g34	integer	1
g36	integer	0
f	matrix	Matrix of size 4×6
t	integer	4
w	integer	0
v	list	Nested 5×3 list
g16	integer	0
g15	integer	-3
g14	integer	0
g13	integer	0
g12	integer	3

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xxxxxxxxxx
 
if(c12=1,1,random(1..4))

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Generated value: `integer`

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Match choices with answers

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$\var{a}$
$\var{b}$
$\var{c}$
$\var{d}$
$\var{f}$

In row echelon form but not reduced
In reduced row echelon form
Neither

For each combination of answer and choice, specify the number of marks to add or subtract when the student picks it.

	In row echelon form but not reduced	In reduced row echelon form	Neither
$\var{a}$
$\var{b}$
$\var{c}$
$\var{d}$
$\var{f}$

Advice

A matrix is in row echelon form if:

- all nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix)

- the leading coefficient (the first nonzero number from the left) of a nonzero row is always strictly to the right of the leading coefficient of the row above it (thus all entries in a column below a leading coefficient are zeros)

- the leading entry of each nonzero row is always 1 (called a leading 1)

A matrix is in reduced row echelon form if the above are all true, but also

-each column containing a leading 1 has zeros everywhere else

We can use these definitions to determine which matrices are in row echelon and reduced row echelon form.

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This question is used in the following exam:

Linear algebra by Simon Thomas in Maths support.

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Simon's copy of Are given matrices in (reduced) row echelon form?

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Simon Thomas 5 years, 9 months ago

Error in variable testing condition

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Generated value: `integer`

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Simon's copy of Are given matrices in (reduced) row echelon form?

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 9 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Match choices with answers

Advanced settings

Generated value: `integer`