Consider the $2\times2$ matrix $B = \begin{pmatrix}4 & a\ b & 1\end{pmatrix}$. (i) State the condition on the real parameters $a$ and $b$ for which $B$ is diagonalizable over $\mathbb{R}$. (ii) For $a=3$ and $b=2$, compute $B^{3}$.

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\begin{pmatrix}118 & 81\ 54 & 37\end{pmatrix}

Neco 2025 Further Mathematics Question 34

Consider the \(2\times2\) matrix \(B = \begin{pmatrix}4 & a\\ b & 1\end{pmatrix}\). (i) State the condition on the real parameters \(a\) and \(b\) for which \(B\) is diagonalizable over \(\\mathbb{R}\). (ii) For \(a=3\) and \(b=2\), compute \(B^{3}\).

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