1. Let \( A=\left[\begin{array}{ccc}1 & 0 & -1 \\ 0 & 1 & 0 \\ 0 & -1\end{array}\right] \) and \( B=\left[\begin{array}{lll}1 & 1 & 2 \\ 1 & 1 & 3 \\ 1 & 1 & 4 \\ 3 & 3 & 1\end{array}\right] \). Compute \( A B \) by the four different ways I introduced. 2. Let \( A=\left[\begin{array}{ccc}0 & -7 & -4 \\ 2 & 4 & 6 \\ 3 & 1 & -1\end{array}\right] \) and \( \boldsymbol{b}=\left[\begin{array}{c}2 \\ 12 \\ -2\end{array}\right] \). Find the reduced row echelon form of the augmented matrix of the matrix equation \( A \boldsymbol{x}=\boldsymbol{b} \) (Hint: You can find the solution in the slide of Week 2, but I still suggest that you do it once again), and do the following: (1) Record each step (the row operation) with a matrix. (2) Suppose you get \( t \) matrices \( M_{1}, M_{2}, \ldots, M_{t} \) in order (you may name it with other names), then (a) Compute \( E=M_{t} M_{t-1} \cdots M_{2} M_{1} \) (Notice the order); (b) Compute \( E A \), and check that if it is an identity matrix. (c) Compute \( E \boldsymbol{b} \), and check that if it equals to the last column vector in the RREF of the augmented matrix.

La ecuación de demanda para un producto es \[ p=60-\frac{50 q}{\sqrt{q^{2}+3600}} \] y la ecuación de oferta es \[ p=10 \ln (q+20)-26 \] Determine el excedente de los consumidores y de los productores bajo equfiblio del mercado. Redondee sus lespuestas al entero más cercano.

\begin{tabular}{l} Downloaded from Stanmorephysics.com \\ 2.4 .4 Write an essay of about one page and explain the causes of Soweto uprising \\ \hline\end{tabular}

1.1) Sea \( F: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2} \) la transformación lineal cuya matriz asociada es: \( M(F)_{B E}=\left(\begin{array}{ccc}-1 & 1 & 0 \\ 2 & 0 & k\end{array}\right) \) siendo \( B=\{(0,1,0),(-1,1,0),(0,0,2)\} \) y \( E \) : base canónica de \( \mathbb{R}^{2} \). 1. Probar que \( F \) es sobreyectiva \( \forall k \in \mathbb{R} \). 2. Obtener el valor de \( k \) para que \( N u(F)=\left\{(x, y, z) \in \mathbb{R}^{3} / 2 x+y=0 \wedge 3 y-z=0\right\} \).

3 From what Tim explains in the movie, what can you infer about the temperature inside a refrigerator? A It's closest to 3 degrees Kelvin (B) It's closest to 3 degrees Fahrenheit (C) It's closest to 3 degrees Celsius : (D)'sclosest to 3 degrees Rankine

In the Soundex Coding System for encoding last names on a Michigan driver's license, the letter s is converted to which number? 3 2 5 1