Assignment:
Q1: Determine if b is a linear combination of a1,a2,a3
(1) (0) (5) (2)
a1 = (-2) , a2= (1) , a3 = (-6) , b= (-1)
(0) (2) (8) (6)
Q2: List five vectors in span { }. For each vector, show the weights on used to generate the vector and list the three entries of the vector. Do not make a sketch.
a)
(7) (-5)
v1= (1) , v2= (3)
(-6) (0)
b)
(3) (-2)
v1 = (0) , v2= (0)
(2) (3)
Q3: Let a1 = (1) a2 = (-2) andb = (4)
(4) (-3) (1)
(-2) (-7) (h)
For what value(s) of h is b in the plane spanned by and ?
Q4: True or false, explain answer.
a) Any list of five real numbers is a vector in .
b) The vector u results when a vector u-v is added to the vector v.
c) The weights in a linear combination cannot all be zero.
d) When u and v are nonzero vectors, Span {u,v} contains the line through u and the origin.
e) Asking whether the linear system corresponding to an augmented matrix [ b] has a solution amounts to asking whether b is in Span { }.