Jika A = \left[\begin{array}{ccc}2&4\\3&1\\\end{array}\right] dan I = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] maka (A - kI) merupakan matriks s

[tex]A = \left[\begin{array}{ccc}2&4\\3&1\\\end{array}\right] \\ I = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] \\ $Agar $(A-kI)$ singular$ \\ A-kI= \left[\begin{array}{ccc}2&4\\3&1\\\end{array}\right]-k\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] \\ A-kI= \left[\begin{array}{ccc}2&4\\3&1\\\end{array}\right]-\left[\begin{array}{ccc}k&0\\0&k\\\end{array}\right] \\ A-kI=\left[\begin{array}{ccc}2-k&4\\3&1-k\\\end{array}\right] \\ |A-kI|=0 \\ (2-k)(1-k)-3.4=0 \\ 2-3k+k^2-12=0 \\ k^2-3k-10=0[/tex]
[tex](k+2)(k-5)=0 \\ k=-2$ dan $k=5[/tex]