If the equations 4a + 9b + 14c = x, 2a + 5b + 8c = y and a + b + c = z have at least one solution for a, b, c and xyz ≠ 0, then which of the following is true?

A. 3x – 5y + 2z = 0
B. 3x – 5y – 2z = 0
C. 2x + 5y – 2z = 0
D. More than one of the above

Question

If the equations 4a + 9b + 14c = x, 2a + 5b + 8c = y and a + b + c = z have at least one solution for a, b, c and xyz ≠ 0, then which of the following is true?



	A. 3x – 5y + 2z = 0
	B. 3x – 5y – 2z = 0
	C. 2x + 5y – 2z = 0
	D. More than one of the above

anonymous · Answer

4a + 9b + 14c = x, 2a + 5b + 8c = y

is ur question??

amistre64 · Answer

i would prolly try something like assuming x y and z are vectors

amistre64 · Answer

<4,9,14> <2,5,8> <1,1,1> im sure theres a null space about this somewheres

anonymous · Answer

http://www.wolframalpha.com/input/?i=4a+%2B+9b+%2B+14c+%3D+x%2C+2a+%2B+5b+%2B+8c+%3D+y plz check ur ans ..in this website..

amistre64 · Answer

4    2   1 = 0
9    5   1 = 0
14  8   1 = 0

forms a matrix that can be rrefed to determine the null space i believe

amistre64 · Answer

rref{{4,2,1,0},{9,5,1,0},{14,8,1,0}} http://www.wolframalpha.com/input/?i=rref%7B%7B4%2C2%2C1%2C0%7D%2C%7B9%2C5%2C1%2C0%7D%2C%7B14%2C8%2C1%2C0%7D%7D we have one free variable in this case such that: c1 = c3 * -3/2 c2 = c3 * 5/2 c3 = c3 * 1 so any scaled value such that c3 <3,-5,-2> is a solution