for these equations
–3x1 – 2x2 + 4x3 = 0
2x1 + x2 – 2x3 = 11
How many solutions does the system have?

Question

for these equations
–3x1	  –	2x2	+	4x3	=	0
2x1	+	x2	–	2x3	=	11
How many solutions does the  system have?

anonymous · Answer

for the first EQN.1  I guess 3..since the highest degree of a polynmomial determines the n solutions fora equation(correct me If I'm wrong/little diverted(just a little :confused:..sry)) and the same is true for the EQN2

anonymous · Answer

well using a matrix and reducing it, gives:

anonymous · Answer

1 	 0 	 0 	 22 
 0 	 1 	 -2 	 -33

anonymous · Answer

so wouldnt x3 be a free variable?

anonymous · Answer

meaning infinetly many solutions

anonymous · Answer

wouldnt it just e one free variable?

rational · Answer

yes when you have more variables compared to equations, there will always be infinitely many solutions if the solutions exist

rational · Answer

Oh yes you're right, one free variable !

rational · Answer

1 	 0 	 0 	 22 
 0 	 1 	 -2 	 -33 
^      ^        ^       

pivot          free

anonymous · Answer

huh...please use WebTEX for modellin equation..I thought it's just a single line EQN.

anonymous · Answer

i figured it out, thanks