Moderate -0.8 This is a straightforward 1-mark multiple choice question requiring only direct substitution of the invariant point into each matrix to check if N(2,-1) = λ(2,-1). It tests basic understanding of eigenvectors but requires minimal calculation and no problem-solving insight, making it easier than average.
4 The point \(( 2 , - 1 )\) is invariant under the transformation represented by the matrix \(\mathbf { N }\) Which of the following matrices could be \(\mathbf { N }\) ?
Circle your answer. [0pt]
[1 mark]
\(\left[ \begin{array} { l l } 4 & 6 \\ 2 & 5 \end{array} \right]\)
\(\left[ \begin{array} { l l } 6 & 5 \\ 4 & 2 \end{array} \right]\)
\(\left[ \begin{array} { l l } 5 & 2 \\ 6 & 4 \end{array} \right]\)
\(\left[ \begin{array} { l l } 2 & 4 \\ 5 & 6 \end{array} \right]\)
4 The point $( 2 , - 1 )$ is invariant under the transformation represented by the matrix $\mathbf { N }$ Which of the following matrices could be $\mathbf { N }$ ?
Circle your answer.\\[0pt]
[1 mark]\\
$\left[ \begin{array} { l l } 4 & 6 \\ 2 & 5 \end{array} \right]$\\
$\left[ \begin{array} { l l } 6 & 5 \\ 4 & 2 \end{array} \right]$\\
$\left[ \begin{array} { l l } 5 & 2 \\ 6 & 4 \end{array} \right]$\\
$\left[ \begin{array} { l l } 2 & 4 \\ 5 & 6 \end{array} \right]$
\hfill \mbox{\textit{AQA Further AS Paper 1 2021 Q4 [1]}}