Read each personality description and then choose the word from the list provided that identifies it. Use a dictionary to define the terms if you need to. melancholic phlegmatic sanguine choleric

The only movies Mr. Ioacca wants to watch are those with unhappy endings.

Find basis and dimension

$$\lbrace{ x \in \Reals^4 | Ax = 0 \rbrace}\ \text{where}\ A = \begin{bmatrix} -1 & 2 & 1 & 2\\ 1 & 1 & 0 & 3 \end{bmatrix}^T$$

Find the volume of cuboid of dimension $3\ \text{cm}\times 5\ \text{cm}\times 3\ \text{cm}$. Where applicable, express answers in terms of $\pi$. Then round to the nearest whole number.

Find the missing dimension of the cone. Round your answer to the nearest tenth. $\text { Volume }=\frac{1}{18} \pi \mathrm{ft}^{3}$, Radius = $\frac{1}{3} f t$, h = ?

In his biography of Samuel Johnson, Boswell recounts many humorous moments and conversations. Look for two or three examples of humor in the excerpts you have read. What part does humor seem to play in Boswell's portrayal of Johnson's personality?

A 4 by 5 inch photo is enlarged by multiplying every dimension by 2 to form a similar 8 by 10 inch photo. What is the ratio of the perimeter of the smaller rectangle to that of larger? Determine the ratio of the two areas.

The matrix $A$ is given. Determine the dimension of (a) Col$A$, (b) Null$A$, (c) Row$A$, and (d) Null$A^T$.

$$\begin{bmatrix}1&&2&&-3\\0&&-1&&-1\\1&&4&&-1\end{bmatrix}$$

Is the given set, taken with the usual addition and scalar multiplication, a vector space? Give reason. If your answer is yes, find the dimension and a basis. All 2x2 matrices [ajk] with a11+a22=0.

Find the dimension of and a basis for the solution space of the system.

$$\quad x_1+i x_2-2 i x_3+x_4=0$$

$$i x_1+3 x_2+4 x_3-2 i x_4=0$$

A matrix is given. State the dimension of the matrix.

$$\left[\begin{array}{rrrr}{1} & {0} & {8} & {0} \\ {0} & {1} & {5} & {-1} \\ {0} & {0} & {0} & {0}\end{array}\right]$$

Find a basis for the span of the set of vectors and finde out what is the dimension of the span if $\mathbf{v}_{1}=(-1,7,7)^{T}, \mathbf{v}_{2}=(-3,8,-4)^{T}$ and $v_{3}=(-4,-14,23)^{T}$.

Is the given set, taken with the usual addition and scalar multiplication, a vector space? Give reason. If your answer is yes, find the dimension and a basis. All polynomials in x of degree 4 or less with nonnegative coefficients.

What is the dimension of the subspace

$$\begin{Bmatrix}\begin{bmatrix}v_1\\v_2\\\vdots\\v_n\end{bmatrix}\in R^n:v_1=0\text{ and }v_2=0\end{Bmatrix}$$

Justify your answer.

A matrix is given. State the dimension of the matrix.

$$\left[\begin{array}{rrrr}{0} & {1} & {-3} & {4} \\ {1} & {1} & {0} & {7} \\ {1} & {2} & {1} & {2}\end{array}\right]$$