Optimization Theory (DS2) HW#1
Basic Matrix and Vector Operations

Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things.”
“I daresay you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”

1. Download and install the programming language R, if you don’t have it. Show me that it works.

2. Write out the transpose of the row vector as a column vector.

3. Add the two vectors

   $$\left(\begin{array}{c}\hfill 1\hfill \\ \hfill 2\hfill \\ \hfill 3\hfill \\ \hfill 4\hfill \end{array}\right)+\left(\begin{array}{c}\hfill 3\hfill \\ \hfill 5\hfill \\ \hfill 7\hfill \\ \hfill 11\hfill \end{array}\right)=\mathrm{?}$$

   (1)

4. Calculate the dot product of the two vectors

   (2)

5. Multiply this vector and matrix

   (3)

6. Multiply these matrices

   (4)