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MATriks
Determinan
2x2
3x3
Penjelasan dengan langkah-langkah:
2. det Kⁿ = (det K)ⁿ
[tex]\sf A = \left[\begin{array}{ccc}-2&3\\1&4\end{array}\right]\to |A|= -2(4) -1(3) = -11[/tex]
[tex]\sf A^2 = \left[\begin{array}{ccc}-2&3\\1&4\end{array}\right].\left[\begin{array}{ccc}-2&3\\1&4\end{array}\right]=\left[\begin{array}{ccc}7&6\\2&19\end{array}\right][/tex]
[tex]|A^2| = 7(19) - 2(6) = 121[/tex]
det A² = (det A)² terbukti
3. Nilai z
[tex]\left|\begin{array}{ccc}z&5&7\\0&z+1&6\\0&0&2z-1\end{array}\right|= 0[/tex]
z(z+ 1)(2z - 1) - 0(5)(2z-1)-0(7) + 0(5(6) -7(z+1) = 0
z(z+ 1)(2z - 1) - 0+ 0 = 0
z(z+ 1)(2z - 1) = 0
z = 0 atau z + 1= 0 atau 2z - 1 =0
z = 0 atau z = - 1 atau z = 1/2
