91Ó°ÊÓ

Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{aligned} -2 x_{1}+4 x_{2}+4 x_{3} &=6 \\ x_{1}-3 x_{2}+2 x_{3} &=1 \end{aligned} $$

Convert the given augmented matrix into a system of linear equations. Use the variables \(x_{1}, x_{2},\) etc. $$\left[\begin{array}{ccccc}1 & 1 & -1 & -1 & 2 \\ 2 & 1 & 3 & 5 & 7\end{array}\right]$$

Find the polynomial with the smallest degree that goes through the given points. $$(-2,14) \text { and }(3,4)$$

State whether or not the given equation is linear. $$x_{1}+y+t=1$$

Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{cc}-5 & 7 \\ 10 & 14\end{array}\right]$$

Find the polynomial with the smallest degree that goes through the given points. $$(1,5),(-1,3) \text { and }(3,-1)$$

Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{array}{l} -x_{1}+2 x_{2}+2 x_{3}=2 \\ 2 x_{1}+5 x_{2}+x_{3}=2 \end{array} $$

State whether or not the given equation is linear. $$\frac{1}{x}+9=3 \cos (y)-5 z$$

Convert the given augmented matrix into a system of linear equations. Use the variables \(x_{1}, x_{2},\) etc. $$\left[\begin{array}{ccccc}1 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & -1 \\ 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 1 & 3\end{array}\right]$$

Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{aligned} -x_{1}-x_{2}+x_{3}+x_{4} &=0 \\ -2 x_{1}-2 x_{2}+x_{3} &=-1 \end{aligned} $$