Suppose N in L(V) is nilpotent. Prove that 0 is only eigenvalue.

Write a paragraph or two comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by appropriate examples.

a quotient of a number and 3, subtracted from 10

5/8x + 3/5 = 8

Find the areas of the shaded parts of the figures in Exercises 62.

[2x 3 3z]=[5 3y 9]

a total of $ 14,000 is invested in two funds paying 4% and 5% annual interest. The combined interest is $620 a)write a system of equations to model this problem b). graph this system and use the graph to estimate how much was invested in each fund?

Let v= [-3 5 5 5] Find a basis of the subspace of R^4 consisting of all vectors perpendicular to v .

Classify each curve. Assume no degenerates. 1) x^2+3y^2+2x+y+1=0 2) 3x^2-2y+4x=6

If, on the first observation, the system is in state 2, what is the probability that it alternates between states 1 and 2 for the first four observations (i.e., it occupies state 2, then state 1, then state 2, and finally state 1 again)?