Problem 11
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{aligned} 2 x_{1}+x_{2}+2 x_{3} &=0 \\ x_{1}+x_{2}+3 x_{3} &=1 \\ 3 x_{1}+2 x_{2}+5 x_{3} &=3 \end{aligned} $$
Problem 11
Perform the given row operations on \(A,\) where $$A=\left[\begin{array}{ccc}2 & -1 & 7 \\ 0 & 4 & -2 \\ 5 & 0 & 3\end{array}\right]$$ $$R_{2} \leftrightarrow R_{3}$$
Problem 11
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{ccc}3 & -3 & 6 \\ -1 & 1 & -2\end{array}\right]$$
Problem 11
Find the polynomial with the smallest degree that goes through the given points. $$(-3,3),(1,3) \text { and }(2,3)$$
Problem 12
Perform the given row operations on \(A,\) where $$A=\left[\begin{array}{ccc}2 & -1 & 7 \\ 0 & 4 & -2 \\ 5 & 0 & 3\end{array}\right]$$ $$R_{1}+R_{2} \rightarrow R_{2}$$
Problem 12
Find the polynomial with the smallest degree that goes through the given points. $$(-2,15),(-1,4),(1,0) \text { and }(2,-5)$$
Problem 12
Solve the system of linear equations. $$ \begin{array}{l} 2 x-3 y=3 \\ 3 x+6 y=8 \end{array} $$
Problem 12
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{array}{l} x_{1}+3 x_{2}+3 x_{3}=1 \\ 2 x_{1}-x_{2}+2 x_{3}=-1 \\ 4 x_{1}+5 x_{2}+8 x_{3}=2 \end{array} $$
Problem 12
Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{ccc}4 & 5 & -6 \\ -12 & -15 & 18\end{array}\right]$$
Problem 13
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{array}{l} x_{1}+2 x_{2}+2 x_{3}=1 \\ 2 x_{1}+x_{2}+3 x_{3}=1 \\ 3 x_{1}+3 x_{2}+5 x_{3}=2 \end{array} $$
