Moderate -0.5 This is a straightforward application of eigenvector properties requiring students to recognize that M²v = 9v and Nv = 4v, then multiply: NM²v = N(9v) = 9Nv = 36v, so λ = 36. While it's a Further Maths topic, it's a single-step conceptual question worth only 1 mark with multiple choice answers, making it easier than average.
The vector \(\mathbf{v}\) is an eigenvector of the matrix \(\mathbf{N}\) with corresponding eigenvalue 4
The vector \(\mathbf{v}\) is also an eigenvector of the matrix \(\mathbf{M}\) with corresponding eigenvalue 3
Given that
$$\mathbf{N}\mathbf{M}^2\mathbf{v} = \lambda\mathbf{v}$$
find the value of \(\lambda\)
Circle your answer.
[1 mark]
10 \(\quad\) 24 \(\quad\) 36 \(\quad\) 144
The vector $\mathbf{v}$ is an eigenvector of the matrix $\mathbf{N}$ with corresponding eigenvalue 4
The vector $\mathbf{v}$ is also an eigenvector of the matrix $\mathbf{M}$ with corresponding eigenvalue 3
Given that
$$\mathbf{N}\mathbf{M}^2\mathbf{v} = \lambda\mathbf{v}$$
find the value of $\lambda$
Circle your answer.
[1 mark]
10 $\quad$ 24 $\quad$ 36 $\quad$ 144
\hfill \mbox{\textit{AQA Further Paper 1 2022 Q4 [1]}}