Linear Algebra Answers

Use the CRAMMER'S RULE to solve these systems of linear equations.

5x+6y+7z=40

2x+4y+2z=34

x+3y+5z=30

Consider the following two functions;

1. f: R-R defined by f(x) = 4x-15.

2. g: RR-defined by f(x) = 15x³.

Prove that both f and g are one-to-one correspondence.

The following data is the input-output tables for different sectors in 

an economy. Find the technology matrix and also the total output against the 

changes in the final demand given:

INDUSTRY X Y FINAL 

DEMAND

X 15 25 40

Y 20 30 50

D=(

50

75)

1. Determine whether the lines given by the equations below are parallel, perpendicular, or neither. Also, find a rigorous algebraic solution for each problem.

a.    b.    c. 

2. A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by. What is the height of the building? What is the maximum height reached by the ball? How long does it take to reach maximum height? Also, find a rigorous algebraic solution for the problem.

3. A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest? Also, find a rigorous algebraic solution for the problem.

(h-50)x+(h+50)y=0

Which of the following matrix (or given expression) results in a non-singular matrix

1) 2 0 0

0 SINà ½SINà

0 -1 -COSà

2) A v B where A = 1 2 -1

3 1 0

-2 -4 2

and B = 1 0 -1

3 1 0

-2 -4 2

3) 2 0 0

3 -4 0

0 -1 0

4) 2 0 0

3 -4 4

0 1 -1

I have 25 coins, x of them are R5 coins and the rest are R2 coins. An expression in term in terms of x for

the number of R2 coins I have is. . .

Find all the third roots of i and plot them on a Argand diagram. (please also state which theorems was used) .

Solve the following question by using bisection method.

upto six iteration

X³ - X - 11 = 0

Use Cramer's rule to find the solution of the following systems of linear equation in terms of the parameter K.

a) 5x - ky = 6. b) 2x - 3y = k

- 2x + 2ky = -3 X + 2y = - 2