1. X adalah matriks persegi ordo 2 yang memenuhi X (1 2) = (4 8 . Matriks X adalah 2 3 5 8) 2. Jika A = (2 4) dan I = (1 0) maka matriks (A - kI) kerupakan

1. [tex]X \left[\begin{array}{ccc}1&2\\2&3\end{array}\right] = \left[\begin{array}{ccc}4&8\\5&8\end{array}\right] [/tex]
 [tex]X = \left[\begin{array}{ccc}4&8\\5&8\end{array}\right] \frac{1}{3-4} \left[\begin{array}{ccc}3&-2\\-2&1\end{array}\right] \\ \\ X = \left[\begin{array}{ccc}4&8\\5&8\end{array}\right] -1 \left[\begin{array}{ccc}3&-2\\-2&1\end{array}\right] \\ \\ X = \left[\begin{array}{ccc}4&8\\5&8\end{array}\right] \left[\begin{array}{ccc}-3&2\\2&-1\end{array}\right] \\ \\ X = \left[\begin{array}{ccc}(4.-3)+(8.2)&(4.2)+(8.-1)\\(5.-3)+(8.2)&(5.2)+(8.-1)\end{array}\right][/tex]
[tex]X = \left[\begin{array}{ccc}4&0\\1&2\end{array}\right][/tex]

2. [tex]\left[\begin{array}{ccc}2&4\\3&1\end{array}\right] - k\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] = 0[/tex] ⇒ [tex]\left[\begin{array}{ccc}2&4\\3&1\end{array}\right] - \left[\begin{array}{ccc}k&0\\0&k\end{array}\right] = 0[/tex]
[tex]\left[\begin{array}{ccc}2-k&4\\3&1-k\end{array}\right] = 0 \\ \\ (2-k)(1-k) - 4.3 = 0 \\ 2 - 2k - k + k^{2} - 12 = 0 \\ -10 - 3k + k^{2} = 0 \\ k^{2} - 3k - 10 = 0 \\ (k+2)(k-5) = 0 \\ k = -2 (atau) k=5[/tex]