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MATH2099-LINALG · Study hub
Topic bank · by knowledge map
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Learning framework
Build knowledge by lecture · open each1Linear systems & matrices
elimination, RREF, solution structure
3 topics
2Vector spaces
subspaces, basis, dimension, span
8 topics
3Linear transformations
linearity, kernel & image, matrix of a map
7 topics
4Orthogonality
orthogonal complement, Gram–Schmidt, projection
5 topics
5Determinants
properties, row ops, product rule
5 topics
6Eigenvalues & diagonalisation
eigenvectors, trace & det, diagonalisability
3 topics
Knowledge map
19 topics → only 10 solution families · open eachFam 1True/False concepts
1 topics
Fam 2Parametric system via det roots
1 topics
Fam 3Subspaces & maps
5 topics
Fam 4Orthogonality: GS / QR / complement
3 topics
Fam 5Eigenvalues: shortcut & full
2 topics
Fam 6Rank–nullity: augmented & geometry
3 topics
Fam 7Determinant properties
1 topics
Fam 8Projection
1 topics
Fam 9Rotation & reflection (paper-only)
1 topics
Fam 10Least squares (paper-only)
1 topics
Topic bank
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Family
Topic 1New
True/False concept statements
49
Topic 2New
Linear system with parameter z
49
Topic 3New
Eigenvectors, trace & determinant
49
Topic 4New
M2,2 subspace + matrix of a linear map
33
Topic 5New
Orthogonal complement basis
26
Topic 6New
QR factorisation & image complement
23
Topic 7New
P2 subspace + matrix of a linear map
16
Topic 8New
Determinant properties
16
Topic 9New
Rank, augmented matrix & solution set
14
Topic 10New
Nullity, augmented matrix & solvable b
10
Topic 15New
Eigenvalues, eigenspaces & diagonalisability
10
Topic 11New
Rank–nullity theorem contradiction
9
Topic 18New
Subspace proof, basis & dimension
8
Topic 19New
Linear map: kernel basis & rank
8
Topic 12New
Projection & projection matrix
7
Topic 17New
Gram–Schmidt orthonormalisation
7
Topic 14New
Least squares fitting
6
Topic 13New
Rotation & reflection matrices
5
Topic 16New
Change of basis & coordinates
5