Discoverand Master Vectors Solutions

Is there a relationship between Facebook use and age among college students? The following two-way table displays data for the 219 students who responded to the survey. $\begin{array}{cc}& \text{Age}\\ \text{Facebook user?}& \begin{array}{lccc}& \begin{array}{c}\text{ Younger }\\ (18-22)\end{array}& \begin{array}{c}\text{ Middle }\\ (23-27)\end{array}& \begin{array}{c}\text{ Older }\\ (28\text{ and up)}\end{array}\\ \text{ Yes }& 78& 49& 21\\ \text{ No }& 4& 21& 46\end{array}\end{array}$

What percent of the students who responded were older Facebook users?

if x, y belong to $R^p$, than is it true that the relation norm $(x+y)=norm(x)+norm(y)$ holds if and only if $x=cyory=cxwithc>0$

Find $|u\cdot v|$ and determine whether $u\cdot v$ 
is pointed at the screen or away from it.
$|u\cdot v|=??$

Assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) the population variance ${\displaystyle {\sigma }^2}$ and (b) the population standard deviation ${\displaystyle \sigma }$. Interpret the results. The final exam scores of 24 randomly selected students in a statistics class are shown in the table at the left. Use a 95% level of confidence.

At the specified position, determine the vectors T, N, and B.
$r(t)=<t^2,\frac{2}{3}{t}^3,t>$ and point $<4,-\frac{16}{3},-2>$

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.
Write the solution in vector form.

$\left[\begin{array}{ccccc}1& 0& 0& -3& 0\\ 0& 1& 0& -4& 0\\ 0& 0& 1& 5& 0\end{array}\right]$

Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.)
$x+2y-z=2,$
$2x-2y+z=1$

Vector Cross Product
Let vectors $A=(1,0,-3),B=(-2,5,1),andC=(3,1,1)$. Calculate the following, expressing your answers as ordered triples (three comma-separated numbers).
(C) $(2\overline{B})(3\overline{C})$
(D) $(\overline{B})(\overline{C})$
(E) $\overrightarrow{A}(\overrightarrow{B}\times \overrightarrow{C})$
(F)If ${\overline{v}}_1\text{ and }{\overline{v}}_2$ are perpendicular, $|{\overline{v}}_1\times {\overline{v}}_2|$
(G) If ${\overline{v}}_1\text{ and }{\overline{v}}_2$ are parallel, $|{\overline{v}}_1\times {\overline{v}}_2|$

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. $\left[\begin{array}{ccc}1& -2& 6\\ 0& 0& 0\end{array}\right]$

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

$\left[\begin{array}{ccc}1& -4& 5\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. $\{\begin{array}{l}7x-5y=11\\ x-y=-5\end{array}$