Diberikan matriks A = ![\left[\begin{array}{ccc}1&1&1\\1&2&t\\1&4& t^{2} \end{array}\right]](https://tex.z-dn.net/?f=+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C1%262%26t%5C%5C1%264%26+t%5E%7B2%7D+%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{ccc}1&1&1\\1&2&t\\1&4& t^{2} \end{array}\right]")
, dengan t bilangan bulat. Matriks A tidak punya invers untuk t =
A. 0 dan 1
B. -1 dan 1
C. -2 dan -1
D. -2 dan 1
E. 1 dan 2
A. 0 dan 1
B. -1 dan 1
C. -2 dan -1
D. -2 dan 1
E. 1 dan 2
izharulhaq78
![\displaystyle \text{matriks tidak memiliki invers apabila determinannya 0}\\\\A=\left[\begin{array}{ccc}1&1&1\\1&2&t\\1&4&t^2\end{array}\right]\\|A|=\left[\begin{array}{ccc}1&1&1\\1&2&t\\1&4&t^2\end{array}\right]\left[\begin{array}{ccc}1&1\\1&2\\1&4\end{array}\right]\\|A|=1\cdot2\cdot t^2+1\cdot t\cdot1+1\cdot1\cdot4-1\cdot2\cdot1-4\cdot t\cdot 1-t^2\cdot1\cdot1\\0=2t^2+t+4-2-4t-t^2\\0=t^2-3t+2\\0=t^2-2t-t+2\\0=(t-2)(t-1)\\t=2\text{ atau }t=1\\\\\boxed{\boxed{HP=\{1,2\}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Ctext%7Bmatriks+tidak+memiliki+invers+apabila+determinannya+0%7D%5C%5C%5C%5CA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C1%262%26t%5C%5C1%264%26t%5E2%5Cend%7Barray%7D%5Cright%5D%5C%5C%7CA%7C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C1%262%26t%5C%5C1%264%26t%5E2%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C1%262%5C%5C1%264%5Cend%7Barray%7D%5Cright%5D%5C%5C%7CA%7C%3D1%5Ccdot2%5Ccdot+t%5E2%2B1%5Ccdot+t%5Ccdot1%2B1%5Ccdot1%5Ccdot4-1%5Ccdot2%5Ccdot1-4%5Ccdot+t%5Ccdot+1-t%5E2%5Ccdot1%5Ccdot1%5C%5C0%3D2t%5E2%2Bt%2B4-2-4t-t%5E2%5C%5C0%3Dt%5E2-3t%2B2%5C%5C0%3Dt%5E2-2t-t%2B2%5C%5C0%3D%28t-2%29%28t-1%29%5C%5Ct%3D2%5Ctext%7B+atau+%7Dt%3D1%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7BHP%3D%5C%7B1%2C2%5C%7D%7D%7D "\displaystyle \text{matriks tidak memiliki invers apabila determinannya 0}\\\\A=\left[\begin{array}{ccc}1&1&1\\1&2&t\\1&4&t^2\end{array}\right]\\|A|=\left[\begin{array}{ccc}1&1&1\\1&2&t\\1&4&t^2\end{array}\right]\left[\begin{array}{ccc}1&1\\1&2\\1&4\end{array}\right]\\|A|=1\cdot2\cdot t^2+1\cdot t\cdot1+1\cdot1\cdot4-1\cdot2\cdot1-4\cdot t\cdot 1-t^2\cdot1\cdot1\\0=2t^2+t+4-2-4t-t^2\\0=t^2-3t+2\\0=t^2-2t-t+2\\0=(t-2)(t-1)\\t=2\text{ atau }t=1\\\\\boxed{\boxed{HP=\{1,2\}}}")
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