Chapter 1

Use Gaussian Elimination to put the given matrix into reduced row echelon form. $$\left[\begin{array}{cc}1 & 2 \\ -3 & -5\end{array}\right]$$

State whether or not the given equation is linear. $$(x-1)(x+1)=0$$

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

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 rescue mission has 85 sandwiches, 65 bags of chips and 210 cookies. They know from experience that men will eat 2 sandwiches, 1 bag of chips and 4 cookies; women will eat 1 sandwich, a bag of chips and 2 cookies; kids will eat half a sandwhich, a bag of chips and 3 cookies. If they want to use all their food up, how many men, women and kids can they feed?

Convert the given augmented matrix into a system of linear equations. Use the variables \(x_{1}, x_{2},\) etc. $$\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 3 & 9\end{array}\right]$$

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

State whether or not the given equation is linear. $$\sqrt{x_{1}^{2}+x_{2}^{2}}=25$$

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

Find the polynomial with the smallest degree that goes through the given points. $$(1,3) \text { and }(3,15)$$

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