Senior Jeopardy

The Matrix

100

Find A+B without using a calculator A=[-1 3] [ 4 0] B=[2 -1] [4 3]

[1 2] [8 3]

200

Find AB without using a calculator A=[-1 4] [ 0 6] B=[3 -1 5] [0 -2 4]

[-3 -7 -11] [ 0 -12 24]

300

Find AB without using a calculator A=[0 1 0] [1 0 0] [0 0 1] B=[ 2 -3 4] [ 1 2 -3] [-2 1 -1]

[ 1 2 -3] [ 2 -3 4] [-2 1 -1]

400

Find the inverse of the matrix: [ 1 2 0 -1] [ 2 -1 1 2] [ 2 0 1 2] [-1 1 1 4]

[-2 -5 6 -1] [ 0 -1 1 0] [10 24 -27 4] [-3 -7 8 -1]

500

Evaluate the determinant of the matrix: [ 1 -3 2] [ 2 4 -1] [-2 0 1]

20

Symptoms of Equations

100

Solve the system: 2x-y=10 3x+2y=1

Solution: x=3 y=-4

200

Solve the Problem: y=x^2 y-9=0

Solution: y=9 x=3

300

Solve the problem algebraically y = x^3 - x^2 y = -2x^2

Solution y=18 x=3

400

Find the Equilibrium point for the given supply and demand curve: p=200-15x p=50+25x

Solution: (3.75,143.75)

500

Use elimination to solve the system of equations: x^2 - 2y = -6 x^2 + y = 4

Solution: (+-[sqrt]2/3 , 10/3)

Casa La De Moivre's

100

What is the trigonometric form of the complex number 2+2i

2sqrt(2)(cos(pi/4)+i(sin(pi/4))

200

Find the product of z1 and z2 in trigonometric form z1=7(cos25+isin25) z2=2(cos130+isin130)

14cos(155* + i sin(155*))

300

Find the trigonometric form of the quotient: 2(cos30*+i sin30) / 3(cos60*+i sin60*)

2/3(cos20*-i sin30*)

400

Use De Moivre's theorem to find the indicated power of the complex number: (1-sqrt(3 i))^3 Write your answer in a+b i form

-8

500

Determine z and the three cube roots of z if one cube root of z is: 1+sqrt(3i)

-8 -2 1+-sqrt(3i)

Hannibal Vector

100

Define a Vector

A quantity with magnitude and direction

200

find the component form and magnitude of the vector PQ if P= (-2,2) Q= (3,4)

Component form: {5,2} Magnitude: sqrt(29)

300

Find a unit vector in the direction of the vector {-2,4}

-.45i + .89j

400

Find the magnitude and direction angle of the vector {3,4}

Magnitude: 5 Direction Angle: 53.13*

500

A force of 50 lbs acts on an object at an angle of 45*. A second force of 75 lbs acts on the object at an angle of -30*. Combine the two vectors and find the resulting force and angle.

Force: 100.33 lbs Angle: -1.22*

Impartial fractions

100

x^2 - 7 / x(x^2 - 4)

(A1/x)+(A2/x-2)+(A3/x+2)

200

x+22/(x+4)(x-2)=A/(x+4)+B/(x-2)^2+C/(x-2)^3

(-3/x+4)+(4/x-2)

300

5x^5+22x^4+36x^3+53x^2+71x+20/(x+3)^2(x^2+2)^2

(2/x+3)+(-1/(x+3))^2+(3x-1/x^2+2)+(x+2/(x^2+2))

400

2/(x-5)(x-3)

(1/x-5)+(-1/x-3)

500

(x^2-x+2)/(x^3-2x^2+x)

(2/x)+(-1/x-1)+(2/(x-1))^2