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Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.
Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.
Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.
The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
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England schools
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England university
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Scotland schools
Taxonomy: mathcentre
Taxonomy: Kind of activity
Taxonomy: Context
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Julia Goedecke
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said | Ready to use | 2 years, 11 months ago |
History
Julia Goedecke 2 years, 11 months ago
Published this.
Julia Goedecke 2 years, 11 months ago
Gave some feedback: Ready to use
Julia Goedecke 2 years, 11 months ago
Created this as a copy of WBQ 9.5 Invertibility via eigenvalues - randomised.| Name | Status | Author | Last Modified | |
|---|---|---|---|---|
| Invertibility via eigenvalues | Ready to use | Julia Goedecke | 07/04/2022 14:34 | |
| Find characteristic polynomial, eigenvalues and eigenvectors of a 2x2 matrix | Ready to use | Julia Goedecke | 21/09/2022 11:48 |
There are 14 other versions that do you not have access to.
| Name | Type | Generated Value |
|---|
| matrixA | matrix |
matrix([0,0],[0,4])
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| a | integer |
0
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| b | number |
4
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| v1 | matrix |
matrix([1],[0])
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| v2 | matrix |
matrix([0],[1])
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| RREFa | matrix |
matrix([0,1],[0,0])
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| RREFb | matrix |
matrix([1,0],[0,0])
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| n | integer |
2
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| P | matrix |
matrix([-1,0],[0,-1])
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| detP | number |
1
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| Pinverse | matrix |
matrix([-1,0],[0,-1])
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| testinverse | matrix |
matrix([1,0],[0,1])
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| invertible | boolean |
false
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| Ainverse | matrix |
matrix([1,0],[0,1])
|
Generated value: matrix
- a
- b
- P
- Pinverse
- Ainverse
- RREFa
- RREFb
This variable doesn't seem to be used anywhere.
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