DP Further Mathematics HL Questionbank

• Syllabus

1.6

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.