91Ó°ÊÓ

Find all the solutions of the systems. \(\left(\begin{array}{rrr}1 & -1 & 2 \\ 2 & 1 & 3 \\ 0 & -1 & 1\end{array}\right)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=O\)

Find all the solutions of the systems. \(\left(\begin{array}{rr}1 & 4 \\ -1 & 1\end{array}\right)\left(\begin{array}{l}x \\ y\end{array}\right)=O\).

Find all the solutions of the systems. \(\left(\begin{array}{ll}6 & 4 \\ 3 & 2\end{array}\right)\left(\begin{array}{l}x \\ y\end{array}\right)=0\).

Find all the solutions of the systems. \(\left(\begin{array}{rrr}2 & 1 & 3 \\ -1 & 1 & 2 \\ 5 & 1 & 4\end{array}\right)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=O\).

Find all the solutions of the systems. \(\left(\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=O .\)

Write the given system of differential equations as a matrix equation. \(\frac{d x}{d t}=2 x+3 y\), \(\frac{d y}{d t}=x-y\)

Write the given system of differential equations as a matrix equation. \(\quad \frac{d x}{d t}=x-y+z+t\) \(\frac{d y}{d t}=x+2 y-z+1\) \(\frac{d z}{d t}=2 x-y+z+e^{t}\)

Write the given system of differential equations as a matrix equation. \(\frac{d x}{d t}=2 x-y+e^{t}\) \(\frac{d y}{d t}=x+y+t\)

Write the given system of differential equations as a matrix equation. \(\quad \frac{d x}{d t}=t x+y+z+\sin t\) \(\frac{d y}{d t}=t^{2} x+t y+1\) \(\frac{d z}{d t}=2 x+y+t z\)