9231 FP2 · Notes & worked examples
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Maths4U Original · Short practice
\(A=\left[\begin{matrix}14 & 1\\1 & 15\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find p.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
\(A=\left[\begin{matrix}15 & 1\\1 & 16\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find p.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Method
Maths4U Original · Short practice
\(A=\left[\begin{matrix}15 & 1\\1 & 16\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find q.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
\(A=\left[\begin{matrix}16 & 1\\1 & 17\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find q.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Apply
Maths4U Original · Short practice
\(A=\left[\begin{matrix}16 & 1\\1 & 17\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find the (1,2) entry of A inverse.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
\(A=\left[\begin{matrix}17 & 1\\1 & 18\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find the (1,2) entry of A inverse.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Check understanding
Maths4U Original · Short practice
\(A=\left[\begin{matrix}17 & 1\\1 & 18\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find the (1,1) entry of A to the fourth power.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Fresh review variant
Maths4U Original · Short practice
\(A=\left[\begin{matrix}18 & 1\\1 & 19\end{matrix}\right]\). Write the characteristic equation as \(\lambda^2-p\lambda+q=0\).
Find the (1,1) entry of A to the fourth power.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.