CAIE A-Level Further Math A2 2.2.4 Eigenvalues and Eigenvectors Questions

Practise finding eigenvalues from characteristic equations and matrix data, checking roots and interpreting the resulting matrix properties with Further Mathematics Paper 2…

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Find eigenvalues from characteristic equations and matrix data.

[Maximum number: 2]

It is given that a is a positive constant.

Show that the eigenvalues of A are a,-1 and -4.

$\left|\begin{array}{ccc}a-\lambda 2 a+5 a+1 0 -4-\lambda 0 3 -1-\lambda\end{array}\right|=0$
Equates determinant to zero.

$(a-\lambda)(-4-\lambda)(-1-\lambda)=0 \Rightarrow \lambda=a,-1,-4$
AG

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CAIE A-Level Further Math A2 2.2.4 Eigenvalues and Eigenvectors Questions question 1