Question

A homogeneous system of equations only has a non-trivial solution if |A| is unequal to 0.

True or false?

If True, is the solution given to IH-3a in the linked problem set wrong?
http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_SupProbSol1.pdf

Answer 1

(Linear Algebra)

Answer 2

true

Answer 3

So the solution would be c has to be unequal to -8 here, no?

Answer 4

-8 it is.

Answer 5

c = -8 to have a non-trivial solution

Answer 6

in that case |A| = 0 though, right?

Answer 7

yes

Answer 8

but if |A|=0 in an homogeneous system of equations, this means that there are infinite solutions, no?

Answer 9

right again

Answer 10

i don't understand the 1H-3a. What is the system?

Answer 11

is it homogeneous?

Answer 12

yes, i'm sorry, the link to the problem is: http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_SupProb1.pdf 1H-3A.

Its homogeneous @myko

Answer 13

@sirm3d so that means that each one of the infinite solutions are non-trivial

Answer 14

yup.

Answer 15

alright, thanks, that was what i was unsure about

Answer 16

the trivial solution is of course x1 = x2 = x3 = 0

Answer 17

yeah got it

Answer 18

for homogeneus system to have a non trivial solution you need vectors that for matrix are linearly dependent. It means |A|=0