Error
There was an error loading the page.
Jim's copy of Frank's copy of Solving system of equations using row operations
This question asks learners to use row operations to find the inverse of a 3x3 matrix.
Metadata
Taxonomy: mathcentre
Taxonomy: Kind of activity
Taxonomy: Context
Contributors
History
Jim Kelly 7 years ago
Created this.There is only one version of this question that you have access to.
Name | Type | Generated Value |
---|
a11 | integer |
10
|
||||
a12 | integer |
4
|
||||
a13 | integer |
4
|
||||
k | integer |
5
|
||||
a21 | integer |
50
|
||||
a22 | integer |
21
|
||||
a23 | integer |
1
|
||||
k1 | integer |
3
|
||||
a31 | integer |
30
|
||||
a32 | integer |
15
|
||||
a33 | integer |
-44
|
||||
k2 | integer |
80
|
||||
k3 | integer |
-19
|
||||
x1 | integer |
3
|
||||
y1 | integer |
1
|
||||
z1 | integer |
5
|
||||
r | integer |
54
|
||||
s | integer |
176
|
||||
t | integer |
-115
|
||||
b23 | integer |
-19
|
||||
b24 | integer |
-94
|
||||
b32 | integer |
3
|
||||
b33 | integer |
-56
|
||||
b34 | integer |
-277
|
||||
c13 | integer |
80
|
||||
c14 | integer |
430
|
||||
c33 | integer |
1
|
||||
c34 | integer |
5
|
||||
d14 | integer |
30
|
||||
d24 | integer |
1
|
||||
d34 | integer |
5
|
Generated value: integer
- a21
- a31
- r
- Statement
- "Unnamed part" - prompt
Parts
-
Gap-fill
-
Gap
Gap 0.
Number entry
-
Gap
Gap 1.
Number entry
-
Gap
Gap 2.
Number entry
-
Gap
Gap 3.
Number entry
-
Gap
Gap 4.
Number entry
-
Gap
Gap 5.
Number entry
-
Gap
Gap 6.
Number entry
-
Gap
Gap 7.
Number entry
-
Gap
Gap 8.
Number entry
-
Gap
Gap 9.
Number entry
-
Gap
Gap 10.
Number entry
-
Gap
Gap 11.
Number entry
-
Gap
Gap 12.
Number entry
-
Gap
Gap 13.
Number entry
-
Gap
Gap 14.
Number entry
-
Gap
Gap 15.
Number entry
-
Gap
Gap 16.
Number entry
-
Gap
Gap 0.
Number entry
Gap-fill
Ask the student a question, and give any hints about how they should answer this part.
First set up the augmented matrix:
(\classjme−var{a11}\classjme−var{a12}\classjme−var{a13}\classjme−var{r}\classjme−var{a21}\classjme−var{a22}\classjme−var{a23}\classjme−var{s}\classjme−var{a31}\classjme−var{a32}\classjme−var{a33}\classjme−var{t})
Use appropriate row operations to get zeroes below the diagonal in the first column:
{a11} | 1 | 2 | 3 |
4 | 5 | 6 | 7 |
8 | 9 | 0 |
\(\left(\begin{array}{rrr|c}\var{a11}&\var{a12}&\var{a13}&\var{r}\\0&1&
Use appropriate row operations to get zeroes above and below the diagonal in the second column:
\(\left(\begin{array}{rrr|c} \var{a11}&0&
Use appropriate row operations to get zeroes above and below the diagonal in the third column:
\(\left(\begin{array}{rrr|c} \var{a11}&0&0&
Hence
x=
y=
z=
Use this tab to check that this question works as expected.
Part | Test | Passed? |
---|---|---|
Gap-fill | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet | ||
Number entry | ||
Hasn't run yet |
This question is used in the following exam: