Identify each underlined verb by writing above it AV for action verb or LV for linking verb.

Example 1. I $\overset{\textit{\color{#c34632}{LV}}}{{\underline{\text{feel}}}\text{}}$ sleepy.

In Madrid, Jody $\underline{\text{stayed}}$ in a youth hostel.

Let A denote an

$$m \times n$$

matrix. (a) Show that null A=null(UA) for every invertible

$$m \times n$$

matrix U. (b) Show that dim(null A)=dim(null(AV)) for every invertible

$$n \times n$$

matrix V. [Hint: If

$$\left\{ \mathbf { x } _ { 1 } , \mathbf { X } _ { 2 } , \dots , \mathbf { X } _ { k } \right\}$$

is a basis of null A, show that

$$\left\{ V ^ { - 1 } \mathbf { x } _ { 1 } , V ^ { - 1 } \mathbf { x } _ { 2 } , \dots , V ^ { - 1 } \mathbf { x } _ { k } \right\}$$

is a basis of null(AV).]

Solve the boundary-value problem, if possible.

$$y’’-8y’+17y=0, y(0)=3, y(π)=2$$

Describe the error in solving the equation. $\frac{1}{x+y}+\frac{1}{x-1}=\frac{2}{(x+1)(x-1)},$ $(x − 1) + (x + 1) = 2,$ $2x = 2,$ $x = 1$ The solution is x = 1.

Show that

$$\left|\begin{array}{ccc} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{array}\right|=a b c+a b+a c+b c$$

Find a solution of the given boundary-value problem. $y^{\prime \prime}+y=1, y(0)=0, y(1)=0$

How do variables, set points, and normal ranges relate to homeostasis?

Graph each of the following functions: $y=\frac{x^{2}-1}{x-1}$. $y=\frac{x^{3}-1}{x-1}$. $y=\frac{x^{4}-1}{x-1}$. $y=\frac{x^{5}-1}{x-1}$. Is x = 1 a vertical asymptote? Why not? What is happening for x = 1? What do you conjecture about $y=\frac{x^{n}-1}{x-1}$, $n \geq 1$ an integer, for x = 1?

Using trapezoids instead of rectangles. That is, on the subinterval $(1 /(n+1), 1 / n)$, let $a_n$ denote the area of the trapezoid having heights $y=1 /(n+1)$ at $x=1 /(n+1)$ and $y=1 / n$ at $x=1 / n$.

Determine the water of hydration for the following hydrates and write the chemical formula.

Ni(NO$_{3}$)$_{2}$ $\sdot$ XH$_{2}$O is found to contain $37.2$% water.

Find the area of each figure.
Trapezoid

Which of the following is the augmented matrix of the system of equations x+2y+z=-1 2x-y+3z=-4? 3x+y-z=-2 (A)

$$\begin{bmatrix}1 & 2 & 1 & -1\\2 & -1 & 3 & -4\\3 & 1 & -1 & -2\end{bmatrix}$$

(B)

$$\begin{bmatrix}1 & 2 & 1 & 1\\2 & -1 & 3 & 4\\3 & 1 & -1 & 2\end{bmatrix}$$

(C)

$$\begin{bmatrix}1 & 2 & 1 & 0\\2 & -1 & 3 & 0\\3 & 1 & -1 & 0\end{bmatrix}$$

(D)

$$\begin{bmatrix}1 & 2 & 1\\2 & -1 & 3\\3 & 1 & -1\end{bmatrix}$$

(E)

$$\begin{bmatrix}1 & 2 & -1\\2 & -1 & -3\\3 & 1 & 1\end{bmatrix}$$

Solve the boundary-value problem, if possible.
$y^{\prime \prime}+y=0, \quad y(0)=1, \quad y(\pi)=0$

Identify each underlined verb by writing above it AV for action verb or LV for linking verb.

Example 1. I $\overset{\textit{\color{#c34632}{LV}}}{{\underline{\text{feel}}}\text{}}$ sleepy.

The Hanson brothers $\underline{\text{are}}$ the best hockey players in the state.