Mark each statement as true or false Justify each answer a T

Mark each statement as true or false. Justify each answer. a. The homogeneous equation A hat x = 0 has the trival solution if and only if the equation has at least one free variable; b. The equation x hat = p hat + tv hat describes a line through and parallel to p hat.

Solution

(A)

False

Reason:

Because each homogeneous equation has the trivial solution x = 0

(B)

False

Reason:

Because this is a line through p parallel to v

if we plug t=0

we get

x=p....which hows it is parallel