Thread: Linear Dependence

I am trying to figure out this problem....I think it should be simple but I am confused...

Are the functions linearly dependent or linearly independent?

y1 = x y2 = absolutevalue(x)


thank you for any help

Originally Posted by khauna

I am trying to figure out this problem....I think it should be simple but I am confused...

Are the functions linearly dependent or linearly independent?

y1 = x y2 = absolutevalue(x)


thank you for any help

I presume you know the defintion of "independenc"?

These functions are linearly independent if and only if the only a, b, such that ay+ by2= ax+ b|x|= 0, for all x, are a= b= 0.

Since that is true for all x, it is true for x= 1 and for x= -1. Put those into the equation and solve the resulting two equations for a and b.

thanks yea that makes sense.