Ex1: A zookeeper wants to give an animal 42 mg of vitamin A and 65 mg of vitamin

Question

Ex1:
A zookeeper wants to give an animal 42 mg of vitamin A and 65 mg of vitamin D er day.he has two supplements: the first contains 10% vitamin A and 25% vitamin D;the second contains 20% vitamin A and 25% vitamin D.How much of each supplement should he give the animal each day?

Ex2:

Find all the solutions to the following systems of linear equations:

{

x1+x2+x3-x4=3

3x1+5x2-2x3+x4=1

-3x1-7x2+7x3-5x4=7

x1+3x2-4x3+3x4=-5

with x1,x2,x3,x4 is variable.

}

Ex3:

If A is a square matrix and A=kAT(A Transpose).show that A=0 if k#+-1.

Explanation / Answer

NOTE: cramster rules only one question per post

let we need x supplement of first and y supplement of second thus

x(0.1A+0.25B) + y(0.2A+0.25B) = 42A + 65 B

equating both sides

0.1x + 0.2y = 42

0.25x+0.25y = 65

now we need to solve both equations

multiply with 4 of quation 2

thus

x+ y = 260 (65*4)

thus

0.1x + 0.2(260-x) = 42

0.1x+52-0.2x = 42

0.1x = 10        => x = 10/0.1 = 100

y = 260-x = 260-100 = 160

thus

we need 100 suplemetn of first and   160 supplemetn of secodn thus ans

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