Bantu Lagi Bray Tolong
A = 3 -1
2 -5
A² = xA+yI dengan x,y∈R dan I = matriks identitas
tentukan nilai x+y
A = 3 -1
2 -5
A² = xA+yI dengan x,y∈R dan I = matriks identitas
tentukan nilai x+y
Takamori37
![\left[\begin{array}{cc}3&-1\\2&-5\end{array}\right]^2=x\left[\begin{array}{cc}3&-1\\2&-5\end{array}\right]+y \left[\begin{array}{cc}1&0\\0&1\end{array}\right]\\\left[\begin{array}{cc}7&2\\-4&23\end{array}\right]=\left[\begin{array}{cc}3x&-x\\2x&-5x\end{array}\right]+\left[\begin{array}{cc}y&0\\0&y\end{array}\right]\\\\\left[\begin{array}{cc}7&2\\-4&23\end{array}\right]=\left[\begin{array}{cc}3x+y&-x\\2x&-5x+y\end{array}\right] \\\\ 2x=-4\\x=-2 \\ \\ 3x+y=7 \\ 3(-2)+y=7 \\ -6+y=7 \\ y=13 \\\\ x+y=-2+13=11](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26-1%5C%5C2%26-5%5Cend%7Barray%7D%5Cright%5D%5E2%3Dx%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%26-1%5C%5C2%26-5%5Cend%7Barray%7D%5Cright%5D%2By++%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%262%5C%5C-4%2623%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3x%26-x%5C%5C2x%26-5x%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dy%260%5C%5C0%26y%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%262%5C%5C-4%2623%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3x%2By%26-x%5C%5C2x%26-5x%2By%5Cend%7Barray%7D%5Cright%5D+%5C%5C%5C%5C+2x%3D-4%5C%5Cx%3D-2+%5C%5C+%5C%5C+3x%2By%3D7+%5C%5C+3%28-2%29%2By%3D7+%5C%5C+-6%2By%3D7+%5C%5C+y%3D13+%5C%5C%5C%5C+x%2By%3D-2%2B13%3D11 "\left[\begin{array}{cc}3&-1\\2&-5\end{array}\right]^2=x\left[\begin{array}{cc}3&-1\\2&-5\end{array}\right]+y \left[\begin{array}{cc}1&0\\0&1\end{array}\right]\\\left[\begin{array}{cc}7&2\\-4&23\end{array}\right]=\left[\begin{array}{cc}3x&-x\\2x&-5x\end{array}\right]+\left[\begin{array}{cc}y&0\\0&y\end{array}\right]\\\\\left[\begin{array}{cc}7&2\\-4&23\end{array}\right]=\left[\begin{array}{cc}3x+y&-x\\2x&-5x+y\end{array}\right] \\\\ 2x=-4\\x=-2 \\ \\ 3x+y=7 \\ 3(-2)+y=7 \\ -6+y=7 \\ y=13 \\\\ x+y=-2+13=11")
1 votes
Thanks 1
Hanjrit
makasih gan
Takamori37
Sip, kelupaan tadi.