week 2 homework update

Author: annadavismath

SYS-0010/main.tex

@@ -29,21 +29,21 @@ \subsection*{Algebra of Linear Systems}
 
 $$ \begin{matrix}
       2x& -&y&=&-4\\
-      7x & +&0y&= &\answer{-7}  
+      7x & +&0y&= &-7  
     \end{matrix}$$
 
 Note that this step eliminates $y$ from the second equation.  
 
 Next we divide both sides of the second equation by $7$. $$\frac{1}{7}R_2\rightarrow R_2$$
 $$\begin{matrix}
        2x& -&y&=&-4\\
-      x & &&= &\answer{-1}
+      x & &&= &-1
 	   \end{matrix}$$
 
 We now know what $x$ is.  Our next goal is to eliminate $x$ from the first equation.  To this end, we subtract twice the second row from the first row and replace the first row with the difference. $$R_1-2R_2\rightarrow R_1$$
 
 $$\begin{matrix}
-	 0x& -&y&=&\answer{-2}\\
+	 0x& -&y&=&-2\\
      x & &&= &-1 \\
     \end{matrix}$$
 
@@ -495,7 +495,7 @@ \subsection*{General Systems of Linear Equations}
 
 \section*{Practice Problems}
 \begin{problem}\label{prob:sysgraphillustration}
-Give a graphical illustration of each of the following scenarios for a system of three equations and two unknowns:
+Give a graphical illustration (draw a picture) for each of the following scenarios for a system of THREE equations and TWO unknowns:
   \begin{enumerate}
   \item The system of three equations is inconsistent, but a combination of any two of the three equations forms a consistent system.
   \item The system is consistent and has a unique solution.
@@ -504,11 +504,10 @@ \section*{Practice Problems}
   \end{enumerate}
 \end{problem}
 
-\emph{Problems \ref{prob:solvesys1}-\ref{prob:solvesys3}}
-
-Solve each system of linear equations or demonstrate that a solution does not exist, and interpret your results geometrically.
 
   \begin{problem}\label{prob:solvesys1}
+Solve the given system of linear equations algebraically or algebraically demonstrate that a solution does not exist.  Interpret your results geometrically.
+  
   $$\begin{array}{ccccc}
       x & +&3y&= &4 \\
 	 x& -&2y&=&-6
@@ -518,6 +517,8 @@ \section*{Practice Problems}
   \end{problem}
 
   \begin{problem}\label{prob:solvesys2}
+Solve the given system of linear equations algebraically or algebraically demonstrate that a solution does not exist.  Interpret your results geometrically.
+  
   $$\begin{array}{ccccc}
       -3x & +&2y&= &7 \\
 	 6x& -&4y&=&5
@@ -526,6 +527,8 @@ \section*{Practice Problems}
 
 
   \begin{problem}\label{prob:solvesys3}
+Solve the given system of linear equations algebraically or algebraically demonstrate that a solution does not exist.  Interpret your results geometrically.
+  
 $$\begin{array}{ccccccc}
       x & -&2y&+&z&= &0 \\
 	 3x& -&2y&+&4z&=&2\\
@@ -534,29 +537,25 @@ \section*{Practice Problems}
 
 Solution:    $$(\answer{4},\answer{1},\answer{-2})$$
 \end{problem}
-
-
- \emph{Problems \ref{prob:sysnosolfindk}-\ref{prob:sysinfmanysolfindk}}
- 
-  Consider the following system of equations.
+    
+     \begin{problem}\label{prob:sysnosolfindk}
+Consider the following system of equations.
   $$\begin{array}{ccccc}
       kx & +&8y&= &4 \\
 	 2x& +&ky&=&-2
     \end{array}$$
-    
-     \begin{problem}\label{prob:sysnosolfindk}
-Find all possible values of k such that this system has no solution.
-
-Solution: $$k=\answer{4}$$
-  \end{problem}
-  
-     \begin{problem}\label{prob:sysinfmanysolfindk}
-Find all possible values of k such that this system has infinitely many solutions.
+     
+\begin{enumerate} 
+\item Find all possible values of $k$ such that this system has no solutions.
 
-Solution: $$k=\answer{-4}$$
-  \end{problem}
+Answer: $$k=\answer{4}$$
 
+\item Find all possible values of k such that this system has infinitely many solutions.
 
+Answer: $$k=\answer{-4}$$
+\end{enumerate}
+  \end{problem}
+  
 \begin{problem}\label{prob:nonzeroprovision}
 Why is there a non-zero provision in Part \ref{item:constantmult} of Definition \ref{def:elemrowops}?  Why is there not a non-zero provision in Part \ref{item:addrow}?
 \end{problem}

SYS-0020/main.tex

@@ -49,13 +49,7 @@ \subsection*{Augmented Matrix Notation}
 
 In this problem, we prompt you to perform elementary row operations on (\ref{eq:sys20originalsystem1}) and ask you to fill in the coefficients in the resulting equations.  This is a multi-step process.  Steps will unfold automatically as you enter correct answers.
 
-\begin{pdfOnly}
-Access interactives through the online version of this text at 
 
-\href{https://ximera.osu.edu/linearalgebradzv3/LinearAlgebraInteractiveIntro}{https://ximera.osu.edu/linearalgebradzv3/LinearAlgebraInteractiveIntro}.
-\end{pdfOnly}
-
-\begin{onlineOnly}
 \begin{problem}
 We start by subtracting twice row 1 from row 2. ($R_2-2R_1\rightarrow R_2$)
 
@@ -127,7 +121,7 @@ \subsection*{Augmented Matrix Notation}
     \end{array}
     \end{equation}
 Now we see that $(-1, -1, 2, 1)$ is the solution.
-\end{onlineOnly}
+
 
 Observe that throughout the entire process, variables $x$, $y$, $z$ and $w$ remained in place; only the coefficients in front of the variables and the entries on the right changed.  Let's try to recreate this process without writing down the variables.  We can capture the original system in (\ref{eq:sys20originalsystem1}) as follows:
 $$\left[\begin{array}{cccc|c}  
@@ -521,11 +515,10 @@ \subsection*{Row-Echelon and Reduced Row-Echelon Forms}
  \end{example}
 
 \section*{Practice Problems}
-\emph{Problems \ref{prob:rrefmultchoice1}-\ref{prob:rrefmultchoice5}}
-
-Determine whether each augmented matrix shown below is in reduced row-echelon form.
 
   \begin{problem}\label{prob:rrefmultchoice1}
+Is the augmented matrix shown below in reduced row-echelon form?  Explain.
+  
   $$\left[\begin{array}{cccc|c}  
  0&1&1&0&2\\1&-3&0&1&4\\0&0&1&0&-1
  \end{array}\right]$$
@@ -536,6 +529,8 @@ \section*{Practice Problems}
   \end{problem}
 
    \begin{problem}\label{prob:rrefmultchoice2}
+Is the augmented matrix shown below in reduced row-echelon form?  Explain.
+   
   $$\left[\begin{array}{cc|c}  
  1&1&1\\0&1&0\\0&0&0
  \end{array}\right]$$
@@ -546,6 +541,8 @@ \section*{Practice Problems}
   \end{problem}
 
   \begin{problem}\label{prob:rrefmultchoice3}
+Is the augmented matrix shown below in reduced row-echelon form?  Explain.
+  
   $$\left[\begin{array}{cc|c}  
  1&0&1\\0&1&0\\0&0&0
  \end{array}\right]$$
@@ -556,6 +553,8 @@ \section*{Practice Problems}
   \end{problem}
 
   \begin{problem}\label{prob:rrefmultchoice4}
+Is the augmented matrix shown below in reduced row-echelon form?  Explain.
+  
   $$\left[\begin{array}{ccc|c}  
  1&0&1&0\\0&1&0&0\\0&0&0&1
  \end{array}\right]$$
@@ -566,6 +565,8 @@ \section*{Practice Problems}
   \end{problem}
 
    \begin{problem}\label{prob:rrefmultchoice5}
+Is the augmented matrix shown below in reduced row-echelon form?  Explain.
+   
   $$\left[\begin{array}{ccc|c}  
  1&1&0&2\\0&1&0&9\\0&0&1&-1
  \end{array}\right]$$
@@ -597,11 +598,9 @@ \section*{Practice Problems}
  \end{multipleChoice}
   \end{problem}
 
-\emph{Problems \ref{prob:sys20solvesys1}-\ref{prob:sys20solvesys2}}
-
-Solve each system of equations.
-
 \begin{problem}\label{prob:sys20solvesys1}
+Solve the system using augmented matrix notation.
+
 $$\begin{array}{ccccccc}
       x & +&3y&-&2z&= &-11 \\
 	 2x& +&y&+&4z&=&12\\
@@ -613,6 +612,8 @@ \section*{Practice Problems}
 \end{problem}
 
 \begin{problem}\label{prob:sys20solvesys2}
+Solve the system using augmented matrix notation.
+
 $$\begin{array}{ccccccc}
       3x & -&y&+&z&= &-5 \\
 	 x& +&2y&-&z&=&-3\\