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 singular untuk nilai k ?
Takamori37
![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](https://tex.z-dn.net/?f=A+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C3%261%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+I+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5C%5C%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%24Agar+%24%28A-kI%29%24+singular%24+%5C%5C+A-kI%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C3%261%5C%5C%5Cend%7Barray%7D%5Cright%5D-k%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+A-kI%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C3%261%5C%5C%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dk%260%5C%5C0%26k%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+A-kI%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2-k%264%5C%5C3%261-k%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%7CA-kI%7C%3D0+%5C%5C+%282-k%29%281-k%29-3.4%3D0+%5C%5C+2-3k%2Bk%5E2-12%3D0+%5C%5C+k%5E2-3k-10%3D0 "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")
0 votes
Thanks 0
annisahuri
terima kasih^^
Takamori37
Iya
