Sketch the following position vectors in R².

Determine the cosines of the angles between the following vectors.

Determine the equation of the polynomial of degree two whose graph passes through the points

(1, 5), (2, 14), (3, 31).

y =

1

If

A = 

2		0
1		3

, B = 

3		1
−2		1

,

and

C = 

1		0
2		3

,

compute each of the following.

Find a single matrix that defines a rotation of the plane through an angle of π/6 about the origin, while at the same time moves points to seven times their original distance from the origin.

 

1		2
3		4

 

The following stochastic matrix P gives the probabilities for a certain region of college and noncollege educated households having at least one college educated child. By a college educated household we understand that at least one parent is college educated, while by noncollege educated we mean that neither parent is college educated. If there are currently 200,000 college educated households and 900,000 noncollege educated households what is the predicted distribution for two generations hence?

1 college educated

2 noncolledge educated

What is the probability that a couple that has no college education will have at least one grandchild with a college education?
3

Let

A = 

1	3	2
1	1	4
6	3	6

.

Find the following minors and cofactors.

Find the coordinate vector of

x² + 2x − 20

relative to the basis

{x² + 1, x + 2, x − 3}.

1

2

3

 

Consider R² with the inner product Determine the equation of the circle with center at the origin and radius one in this space. (Use x₁ and x₂ for the variables.)

1

= 1

Sketch the circle.

Maximize

f = 8x + 4y

subject to

f

=

1