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The cat food is sold in tins containing 500 g.

Write down the matrix M such that the product XM will show, for each brand,

the total cost, in cents, of buying ten tins at both stores during May.

Find all values of lemth€C such that lemth(1+2i, 5+4i) =(3+2i, 6-i)

Show that in the definition of a vector space v the condition about existence of additive inverse can be replaced with the condition:0v=v for all v€V

What are the domain and range for these equations?

1. f(x)= square root of (x-1)
2. f(x)=6x-1/1-2x
3. the inverse of function f(x) = square root of (x-1)

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

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