DP Further Mathematics HL Questionbank

• Syllabus

1.1

Sub sections and their related questions

Definition of a matrix: the terms element, row, column and order for \(m \times n\) matrices.

• SPNone.1.hl.TZ0.12a: (i)     Find the matrices \({\boldsymbol{A}^2}\) and \({\boldsymbol{A}^3}\) , and verify that...
• SPNone.1.hl.TZ0.12b: (i)     Suggest a similar expression for \({\boldsymbol{A}^n}\) in terms of \(\boldsymbol{A}\)...
• 14M.1.hl.TZ0.10: The matrix A is given by A =...
• 16M.1.hl.TZ0.14a: (i)     Explain why M is a square matrix. (ii)     Find the set of possible values of det(M).
• 18M.1.hl.TZ0.2a: Show that A4 = 12A + 5I.
• 18M.1.hl.TZ0.2b: Let B = \(\left[ {\begin{array}{*{20}{c}} 4&2 \\ 1&{ - 3} \end{array}} \right]\). Given...
• 18M.1.hl.TZ0.10c: A matrix M is said to be orthogonal if M TM = I where I is the identity. Show that Q is orthogonal.

Algebra of matrices: equality; addition; subtraction; multiplication by a scalar for \(m \times n\) matrices.

• 18M.1.hl.TZ0.2a: Show that A4 = 12A + 5I.
• 18M.1.hl.TZ0.2b: Let B = \(\left[ {\begin{array}{*{20}{c}} 4&2 \\ 1&{ - 3} \end{array}} \right]\). Given...
• 18M.1.hl.TZ0.10c: A matrix M is said to be orthogonal if M TM = I where I is the identity. Show that Q is orthogonal.

Multiplication of matrices.

• 18M.1.hl.TZ0.2a: Show that A4 = 12A + 5I.
• 18M.1.hl.TZ0.2b: Let B = \(\left[ {\begin{array}{*{20}{c}} 4&2 \\ 1&{ - 3} \end{array}} \right]\). Given...
• 18M.1.hl.TZ0.10c: A matrix M is said to be orthogonal if M TM = I where I is the identity. Show that Q is orthogonal.

Properties of matrix multiplication: associativity, distributivity.

• 16M.1.hl.TZ0.14a: (i)     Explain why M is a square matrix. (ii)     Find the set of possible values of det(M).
• 18M.1.hl.TZ0.2a: Show that A4 = 12A + 5I.
• 18M.1.hl.TZ0.2b: Let B = \(\left[ {\begin{array}{*{20}{c}} 4&2 \\ 1&{ - 3} \end{array}} \right]\). Given...
• 18M.1.hl.TZ0.10c: A matrix M is said to be orthogonal if M TM = I where I is the identity. Show that Q is orthogonal.

Identity and zero matrices.

• 18M.1.hl.TZ0.2a: Show that A4 = 12A + 5I.
• 18M.1.hl.TZ0.2b: Let B = \(\left[ {\begin{array}{*{20}{c}} 4&2 \\ 1&{ - 3} \end{array}} \right]\). Given...
• 18M.1.hl.TZ0.10c: A matrix M is said to be orthogonal if M TM = I where I is the identity. Show that Q is orthogonal.

Transpose of a matrix including \({A^{\text{T}}}\) notation: \({(AB)^{\text{T}}} = {B^{\text{T}}}{A^{\text{T}}}\) .

• 15M.2.hl.TZ0.7a: (i)     Show that \({({A^T})^{ - 1}} = {({A^{ - 1}})^T}\). (ii)     Show that...
• 15M.2.hl.TZ0.7b: A relation \(R\) is defined on \(S\) such that \(A\) is related to \(B\) if and only if there...
• 18M.1.hl.TZ0.2a: Show that A4 = 12A + 5I.
• 18M.1.hl.TZ0.2b: Let B = \(\left[ {\begin{array}{*{20}{c}} 4&2 \\ 1&{ - 3} \end{array}} \right]\). Given...
• 18M.1.hl.TZ0.10c: A matrix M is said to be orthogonal if M TM = I where I is the identity. Show that Q is orthogonal.