Activity 2.1.1. Testing Interactive and Response together.
Some text.
Section 2.1 Testing things
Activity 2.1.3. Testing tabs and prefigure.
testing the intro
(a)
With annotations
Diagram Exploration Keyboard Controls
(b)
With annotations and dimensions changed to (200,200).
Diagram Exploration Keyboard Controls
(c)
Without annotations
Worksheet Participate
Objectives
- Identify matrices in reduced row echelon form and row echelon form
- Use Gauss-Jordan elimination to put matrices into reduced row echelon form
1. Why rref?
Write the associated system of linear equations for each of the matrices below.
\(\begin{bmatrix} 1 \amp 2 \amp 3 \amp 4 \\ 2 \amp -1 \amp 3 \amp 0 \\ 3 \amp 1 \amp 5 \amp 3 \end{bmatrix}\)
\(\begin{bmatrix} 1 \amp 0 \amp 0 \amp 4 \\ 0 \amp 1 \amp 0 \amp 0 \\ 0 \amp 0 \amp 1 \amp 3 \end{bmatrix}\)
Which system of equations would you prefer to be asked to solve on an exam?
2. Gauss-Jordan algorithm.
Use Gauss-Jordan elimination to put each of the matrices below into reduced row echelon form.
a.
\begin{equation*}
\begin{bmatrix} 2 \amp 5 \amp -3 \\ 5 \amp -5 \amp -25 \end{bmatrix}
\end{equation*}
b.
\begin{equation*}
\begin{bmatrix} 2 \amp 5 \amp -3 \\ 2 \amp 5 \amp 1 \end{bmatrix}
\end{equation*}
c.
\begin{equation*}
\begin{bmatrix} 1\amp 2 \amp 3 \amp 5 \\ 0 \amp 4 \amp 5 \amp 7 \\ 1 \amp 6 \amp 9 \amp 11 \end{bmatrix}
\end{equation*}
3. Form of matrices.
For each of the following matrices, say if it is in reduced row echelon form. If it isn’t, say whether it is in row echelon form or if it’s in neither form.
a.
\(\left[\begin{array}{ccc} 1\amp 0 \amp -3\\0\amp 1 \amp 1\\ \end{array} \right]\)
b.
\(\left[\begin{array}{cc} 1\amp 2\\0\amp 0\\ \end{array} \right]\)
c.
\(\left[\begin{array}{ccc} 1\amp 1 \amp -3\\0\amp 0 \amp 1\\ \end{array} \right]\)
d.
\(\begin{bmatrix} 1\amp 0 \amp -3\\0\amp 0 \amp 0\\ 0 \amp 1 \amp 3 \end{bmatrix}\)
e.
\(\begin{bmatrix} 1\amp 0 \amp 0 \amp 4 \amp 5 \\0\amp 0 \amp 1 \amp 2 \amp 7 \\ 0 \amp 1 \amp 0 \amp 3 \amp 11 \end{bmatrix}\)
f.
\(\begin{bmatrix} 1\amp 0 \amp 0 \amp 5 \\0\amp 4 \amp 0 \amp 7 \\ 0 \amp 0 \amp 1 \amp 11 \end{bmatrix}\)
g.
\(\begin{bmatrix} 1\amp 0 \amp 0 \amp 5 \\0\amp 1 \amp 0 \amp 7 \\ 0 \amp 0 \amp 1 \amp 11 \end{bmatrix}\)
h.
\(\begin{bmatrix} 1\amp 0 \amp 3 \amp 0 \amp 6 \\0\amp 1 \amp -1 \amp 0 \amp -23 \\ 0 \amp 0 \amp 0 \amp 1 \amp 11 \end{bmatrix}\)
4.
Activity 2.1.4. Non 1-1 Matching Problem, Function Types.
Activity 2.1.5. How a matrix is indexed, old markup.
In the matrix
\begin{equation*}
A=\begin{bmatrix} 2 \amp -1 \amp 3 \amp 5 \\ 0 \amp 3\amp 6\amp -3 \\ 4 \amp -2 \amp 7 \amp 5 \end{bmatrix}
\end{equation*}
what is \(a_{23}\text{?}\)
Activity 2.1.6. How a matrix is indexed, new markup.
Activity 2.1.7. Solve a fruit puzzle, image child of paragraph.
Activity 2.1.8. Solve a fruit puzzle, image child of figure.
Activity 2.1.10. Solve a fruit puzzle, image child of statement.
Activity 2.1.11. MultiAnswer, and the logical “and”.
This problem uses a MultiAnswer, where multiple blanks are needed for the right answer. Since the checking of these problems often involves logic, we also demonstrate how to replace the perl “and” in the pretext source, since ampersands are reserved characters.
Enter two numbers that are equal, and the first one must be a 2: \(=\)
