Problem 3
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{aligned} x_{1}+x_{2} &=3 \\ 2 x_{1}+x_{2} &=4 \end{aligned} $$
Problem 3
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 carpenter can make two sizes of table, grande and venti. The grande table requires 4 table legs and 1 table top; the venti requires 6 table legs and 2 table tops. After doing work, he counts up spare parts in his warehouse and realizes that he has 86 table tops left over, and 300 legs. How many tables of each kind can he build and use up exactly all of his materials?
Problem 3
State whether or not the given matrices are in reduced row echelon form. If it is not, state why. (a) \(\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]\) (b) \(\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0\end{array}\right]\) (c) \(\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0\end{array}\right]\) (d) \(\left[\begin{array}{cccc}1 & 0 & 0 & -5 \\ 0 & 1 & 0 & 7 \\ 0 & 0 & 1 & 3\end{array}\right]\)
Problem 3
Convert the given system of linear equations into an augmented matrix. $$ \begin{aligned} x_{1}+3 x_{2}-4 x_{3}+5 x_{4} &=17 \\ -x_{1}+4 x_{3}+8 x_{4} &=1 \\ 2 x_{1}+3 x_{2}+4 x_{3}+5 x_{4} &=6 \end{aligned} $$
Problem 3
State whether or not the given equation is linear. $$-3 x+9=3 y-5 z+x-7$$
Problem 4
Find the solution to the given linear system. If the system has infinite solutions, give 2 particular solutions. $$ \begin{array}{c} -3 x_{1}+7 x_{2}=-7 \\ 2 x_{1}-8 x_{2}=8 \end{array} $$
Problem 4
State whether or not the given matrices are in reduced row echelon form. If it is not, state why. (a) \(\left[\begin{array}{llll}2 & 0 & 0 & 2 \\ 0 & 2 & 0 & 2 \\ 0 & 0 & 2 & 2\end{array}\right]\) (b) \(\left[\begin{array}{llll}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0\end{array}\right]\) (c) \(\left[\begin{array}{cccc}0 & 0 & 1 & -5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right]\) (d) \(\left[\begin{array}{llllll}1 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0\end{array}\right]\)
Problem 4
Convert the given system of linear equations into an augmented matrix. $$ \begin{aligned} 3 x_{1}-2 x_{2} &=4 \\ 2 x_{1} &=3 \\ -x_{1}+9 x_{2} &=8 \\ 5 x_{1}-7 x_{2} &=13 \end{aligned} $$
Problem 4
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 jar contains 100 marbles. We know there are twice as many green marbles as red; that the number of blue and yellow marbles together is the same as the number of green; and that three times the number of yellow marbles together with the red marbles gives the same numbers as the blue marbles. How many of each color of marble are in the jar?
Problem 4
State whether or not the given equation is linear. $$\sqrt{5} y+\pi x=-1$$
