Problem 1
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{array}{l} 2 x_{1}+4 x_{2}=2 \\ x_{1}+2 x_{2}=1 \end{array} $$
Problem 1
Convert the given system of linear equations into an augmented matrix. $$ \begin{array}{l} 3 x+4 y+5 z=7 \\ -x+y-3 z=1 \\ 2 x-2 y+3 z=5 \end{array} $$
Problem 1
Find the solution of the given problem by: (a) creating an appropriate system of linear equations (b) forming the augmented matrix that corresponds to this system (c) putting the augmented matrix into reduced row echelon form (d) interpreting the reduced row echelon form of the matrix as a solution. A farmer looks out his window at his chickens and pigs. He tells his daughter that he sees 62 heads and 190 legs. How many chickens and pigs does the farmer have?
Problem 1
State whether or not the given matrices are in reduced row echelon form. If it is not, state why. (a) \(\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\) (b) \(\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\) (c) \(\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]\) (d) \(\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]\)
Problem 1
State whether or not the given equation is linear. $$x+y+z=10$$
Problem 2
State whether or not the given equation is linear. $$x y+y z+x z=1$$
Problem 2
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{array}{l} -x_{1}+5 x_{2}=3 \\ 2 x_{1}-10 x_{2}=-6 \end{array} $$
Problem 2
Find the solution of the given problem by: (a) creating an appropriate system of linear equations (b) forming the augmented matrix that corresponds to this system (c) putting the augmented matrix into reduced row echelon form (d) interpreting the reduced row echelon form of the matrix as a solution. A lady buys 20 trinkets at a yard sale. The cost of each trinket is either $$\$ 0.30$$ or $$\$ 0.65 .$$ If she spends $$\$ 8.80$$, how many of each type of trinket does she buy?
Problem 2
Convert the given system of linear equations into an augmented matrix. $$ \begin{array}{l} 2 x+5 y-6 z=2 \\ 9 x\quad-8 z=10 \\ -2 x+4 y+z=-7 \end{array} $$
Problem 2
State whether or not the given matrices are in reduced row echelon form. If it is not, state why. (a) \(\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]\) (b) \(\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 1\end{array}\right]\) (c) \(\left[\begin{array}{lll}0 & 0 & 0 \\ 1 & 0 & 0\end{array}\right]\) (d) \(\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]\)
