DP Further Mathematics HL Questionbank
1.6
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Description
Linear transformations:
T(u + v) = T(u) + T(v), T(ku) = kT(u).
Directly related questions
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 15M.1.hl.TZ0.12b: (i) State the column rank of \(M\). (ii) Find the basis for the range of this...
Sub sections and their related questions
Linear transformations: \(T(u + v) = T(u) + T(v)\) , \(T(ku) = kT(u)\) .
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
Composition of linear transformations.
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
Domain, range, codomain and kernel.
- 15M.1.hl.TZ0.12b: (i) State the column rank of \(M\). (ii) Find the basis for the range of this...
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
Result and proof that the kernel is a subspace of the domain.
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
Result and proof that the range is a subspace of the codomain.
- 15M.1.hl.TZ0.12b: (i) State the column rank of \(M\). (ii) Find the basis for the range of this...
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
Rank-nullity theorem (proof not required).
- 18M.1.hl.TZ0.10a.i: determine the 2 × 2 matrix P which represents a reflection in the...
- 18M.1.hl.TZ0.10a.ii: determine the 2 × 2 matrix Q which represents an anticlockwise rotation of θ about the origin.
- 18M.1.hl.TZ0.10b: Describe the transformation represented by the matrix PQ.
