Matrices: past paper questions

Where the questions come from

• Question 8May/June 2025, paper 21Structured13 marks

  It is given that $\lambda$ is an eigenvalue of the non-singular square matrix $\mathbf{A}$, with corresponding eigenvector $\mathbf{e}$. Show that $\mathbf{e}$ is an eigenvector of ${\mathbf{A}}^3$ with corresponding eigenvalue ${\lambda }^3$.

  Try this question
• Question 8May/June 2024, paper 23Structured14 marks

  The planes ${\mathrm{\Pi }}_1$ and ${\mathrm{\Pi }}_2$ do not intersect and are both perpendicular to $\mathbf{i}+2\mathbf{j}+3\mathbf{k}$. The line $l$ intersects ${\mathrm{\Pi }}_1$ at the point $(1,6,0)$ and intersects ${\mathrm{\Pi }}_2$ at the point $(3,-6,0)$. Find Cartesian equations of ${\mathrm{\Pi }}_1$ and ${\mathrm{\Pi }}_2$.

  Try this question