Diketahui matriks A =![\left[\begin{array}{ccc}6&-2\\-6&5\\\end{array}\right]](https://tex.z-dn.net/?f=+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%5C%5C-6%265%5C%5C%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{ccc}6&-2\\-6&5\\\end{array}\right]")
jika matriks ( A-kl) adalah matriks singular, nilai k adalah
Takamori37
Singular artinya Determinannya jadi 0
![\left[\begin{array}{cc}6&-2\\-6&5\end{array}\right] +k \left[\begin{array}{cc}1&0\\0&1\end{array}\right]= \left[\begin{array}{cc}6&-2\\-6&5\end{array}\right]+ \left[\begin{array}{cc}k&0\\0&k\end{array}\right] \\ \\ \left|\begin{array}{cc}6+k&-2\\-6&5+k\end{array}\right| =0 \\ \\ (6+k)(5+k)-(-6)(-2)=0 \\ 30+11k+k^2-12=0 \\ k^2+11k+18=0 \\ (k+9)(k+2)=0 \\ k=-9$ dan $k=-2](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-2%5C%5C-6%265%5Cend%7Barray%7D%5Cright%5D+%2Bk++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-2%5C%5C-6%265%5Cend%7Barray%7D%5Cright%5D%2B++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dk%260%5C%5C0%26k%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%5C%5C++%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D6%2Bk%26-2%5C%5C-6%265%2Bk%5Cend%7Barray%7D%5Cright%7C+%3D0+%5C%5C++%5C%5C+%286%2Bk%29%285%2Bk%29-%28-6%29%28-2%29%3D0+%5C%5C+30%2B11k%2Bk%5E2-12%3D0+%5C%5C+k%5E2%2B11k%2B18%3D0+%5C%5C+%28k%2B9%29%28k%2B2%29%3D0+%5C%5C+k%3D-9%24+dan+%24k%3D-2 "\left[\begin{array}{cc}6&-2\\-6&5\end{array}\right] +k \left[\begin{array}{cc}1&0\\0&1\end{array}\right]= \left[\begin{array}{cc}6&-2\\-6&5\end{array}\right]+ \left[\begin{array}{cc}k&0\\0&k\end{array}\right] \\ \\ \left|\begin{array}{cc}6+k&-2\\-6&5+k\end{array}\right| =0 \\ \\ (6+k)(5+k)-(-6)(-2)=0 \\ 30+11k+k^2-12=0 \\ k^2+11k+18=0 \\ (k+9)(k+2)=0 \\ k=-9$ dan $k=-2")
7 votes
Thanks 14
dimasqomarouq4fw
Dipertanyaannya (A-kI), kenapa di jawaban menjadi (A+kI)?
Denikurnia11
matriks L dapat dimna