DP Further Mathematics HL Questionbank

• Syllabus

1.9

Sub sections and their related questions

Eigenvalues and eigenvectors of \(2 \times 2\) matrices.

• SPNone.2.hl.TZ0.8a: Given that the elements of a \(2 \times 2\) symmetric matrix are real, show that   (i)     the...
• SPNone.2.hl.TZ0.8b: The matrix \(\boldsymbol{A}\) is given...
• 14M.1.hl.TZ0.4: The matrix M is defined by M =...
• 16M.1.hl.TZ0.14b: (i)     Find the value of \(a\). (ii)     Find the eigenvalues of N. (iii)     Find...
• 18M.1.hl.TZ0.13c: State the two eigenvalues of M.
• 18M.1.hl.TZ0.13d: State two eigenvectors of M which correspond to the two eigenvalues.

Characteristic polynomial of \(2 \times 2\) matrices.

• 18M.1.hl.TZ0.13c: State the two eigenvalues of M.
• 18M.1.hl.TZ0.13d: State two eigenvectors of M which correspond to the two eigenvalues.

Diagonalization of \(2 \times 2\) matrices (restricted to the case where there are distinct real eigenvalues).

• 18M.1.hl.TZ0.13c: State the two eigenvalues of M.
• 18M.1.hl.TZ0.13d: State two eigenvectors of M which correspond to the two eigenvalues.

Applications to powers of \(2 \times 2\) matrices.

• 18M.1.hl.TZ0.13c: State the two eigenvalues of M.
• 18M.1.hl.TZ0.13d: State two eigenvectors of M which correspond to the two eigenvalues.