91Ó°ÊÓ

Find the polynomial with the smallest degree that goes through the given points. $$(-2,-7),(1,2),(2,9) \text { and }(3,28)$$

Solve the system of linear equations. $$ \begin{array}{c} x-y+z=1 \\ 2 x+6 y-z=-4 \\ 4 x-5 y+2 z=0 \end{array} $$

Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{ccc}-2 & -4 & -8 \\ -2 & -3 & -5 \\ 2 & 3 & 6\end{array}\right]$$

Perform the given row operations on \(A,\) where $$A=\left[\begin{array}{ccc}2 & -1 & 7 \\ 0 & 4 & -2 \\ 5 & 0 & 3\end{array}\right]$$ $$2 R_{2}+R_{3} \rightarrow R_{3}$$

Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{aligned} 2 x_{1}+4 x_{2}+6 x_{3} &=2 \\ 1 x_{1}+2 x_{2}+3 x_{3} &=1 \\ -3 x_{1}-6 x_{2}-9 x_{3} &=-3 \end{aligned} $$

Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 1 & 1 \\ 2 & 1 & 2\end{array}\right]$$

Find the polynomial with the smallest degree that goes through the given points. $$(-3,10),(-1,2),(1,2) \text { and }(2,5)$$

Perform the given row operations on \(A,\) where $$A=\left[\begin{array}{ccc}2 & -1 & 7 \\ 0 & 4 & -2 \\ 5 & 0 & 3\end{array}\right]$$ $$\frac{1}{2} R_{2} \rightarrow R_{2}$$

Solve the system of linear equations. $$ \begin{aligned} x+y-z &=1 \\ 2 x+y &=2 \\ y+2 z &=0 \end{aligned} $$

Perform the given row operations on \(A,\) where $$A=\left[\begin{array}{ccc}2 & -1 & 7 \\ 0 & 4 & -2 \\ 5 & 0 & 3\end{array}\right]$$ $$-\frac{5}{2} R_{1}+R_{3} \rightarrow R_{3}$$