Given

$$A=\left[\begin{array}{cc}3 & -2 \\ 1 & 0 \\ 0 & 5\end{array}\right], B=\left[\begin{array}{cc}4 & -5 \\ 3 & 0 \\ -2 & 2\end{array}\right], C=\left[\begin{array}{cc}2 & -1 \\ 6 & 10 \\ -3 & 7\end{array}\right]$$

, and

$$D=\left[\begin{array}{ccc}3 & 2 & 5 \\ -2 & -4 & 1\end{array}\right]$$

, determine the following, if possible. See the earlier examples.

$$3 C-A$$

Find $a_2$ and $a_3$ for the geometric sequence.

$$2, a_2, a_3,-54$$

Complete the sentence by writing out the correct time according to the cue.

(1:00 a.m.) II est $\rule{1cm}{0.2pt}$ une heure du matin.

¿Cuál de las dos palabras 'pero' o 'sino' completa la frase?
No sólo se ven cráteres en la luna ____ también vastos mares.

Find the minimal polynomial of each of the following matrices. $\\$ (a)$

$$\left(\begin{array}{ll}{2} & {1} \\ {1} & {2}\end{array}\right)$$

$(b)$

$$\left(\begin{array}{ll}{1} & {1} \\ {0} & {1}\end{array}\right)$$

$(c)$

$$\left(\begin{array}{ccc}{4} & {-14} & {5} \\ {1} & {-4} & {2} \\ {1} & {-6} & {4}\end{array}\right)$$

$(d)$

$$\left(\begin{array}{rrr}{3} & {0} & {1} \\ {2} & {2} & {2} \\ {-1} & {0} & {1}\end{array}\right)$$

$

Use the given LU factorization to find all solutions to $Ax = b.$

$$A=\left[\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ -1 & 3 & 1 & 0 \\ -3 & 0 & 0 & 1 \end{array}\right]\left[\begin{array}{ccc} 1 & 3 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right], \ \mathbf{b}=\left[\begin{array}{r} -1 \\ -3 \\ -2 \\ 3 \end{array}\right]$$

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word.

Joe's condition regressed at the hospital because...

In this exercise, evaluate (if possible) the sine, cosine, and tangent of the real number.

$$t=\dfrac{\pi}{3}$$

Find the sine, cosine, and tangent of each angle.

$$780^\circ$$

$$-150^\circ$$

$$-405^\circ.$$

Find $a_5$ and $a_n$ for each geometric sequence.

$$-2,6,-18,54, \ldots$$

Solve the inequalities both algebraically and graphically:

$$18 \leq 2 x+6<42$$

Indica a qué o a quién se refiere cada pronombre subrayado en estos relatos periodísticos.

Dos fanáticos comentaron: "No nos llamó la atención.

Escribe dos cualidades distintas y dos especialidades o cursos que crees tú que un banco busca en un empleado.

For each item listed, say whether it is found in your classroom. If it is, include how many. Follow the model. Modelo: mapa: Hay dos mapas. / No hay un mapa.

puerta: