Please answer questions 1 and 2 on page 1 and questions 3 and 4 on page 2. Let A= .  1. Find all the eigenvalues of A.   (7 points) 2. Find the corresponding eigen vectors.   (7 points) 3. Can A be diagonalized?   (2 points) 4. If the answer to 3 is yes, find a matrix X and a diagonal matrix D so that X^{-1}*A*X is a diagonal matrix D. (4 points) Old Quiz 6: ————- 1.  Use Cramer’s rule to find the solutions of the system of equations: x1+ 3×2+ x3=1 2×1+x2+x3  =5 -2×1+2×2 – x3= -8   This can broken into the following subproblems: (i) Compute the determinant of the coefficient matrix for the system of equations above.  (5 points) (ii) Compute the determinant of the three matrices obtained by replacing one column of the coefficient matrix by the vector on the right hand side.  (4 points each) (iii) Write the solutions for each of the variables x1, x2 and x3. (3 points)    

Your answer to the following question should consist of a single word. An interspecific interaction in which both species benefit is known as: 

Bonus Question: 1 pt What was your favorite part of the class?

Predation of a rat by a snake can be categorized as an ______ interaction.

Penguins that live in the South Pole must deal with the freezing temperature and cold winds. What type of ecological factor is this?

Sponges are different from all other animals in that they lack true _____. (Your answer should consist of a single word.)

The arachnids (spiders, scorpions, ticks) are the most successful arthropod group.

Exploring the tropics, you discover a nonvascular plant that produces pollen. What type of plant have you discovered?

Which is not a characteristic of the phylum Platyhelminthes (flatworms)?

Metamorphosis of bees includes the following stages: egg, larva, pupa, adult.  What type of metamorphosis has just been described?