True/False Answer the following by circling T(=true) or F(=false). Justify your
ID: 3120381 • Letter: T
Question
True/False Answer the following by circling T(=true) or F(=false). Justify your answer for full credit.
(a) T F Whenever a system has free variables, the solution set contains many solutions.
(b) T F When u and v are nonzero vectors, Span{u, v} contains the line through u and the origin.
(c) T F Asking whether the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution amounts to asking whether b is in Span{a1, a2, a3}.
(d) T F If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A.
(e) T F If A is an m × n matrix whose columns do not span R m then the equation Ax = b is inconsistent for some b in R m.
(f) T F The equation Ax = b is homogeneous if the zero vector is a solution.
(g) T F The columns of any 4 × 5 matrix are linearly dependent.
Explanation / Answer
a) Whenever a system has free variables, the solution set contains many solutions.
Answer: Flase
b) When u and v are nonzero vectors, Span{u, v} contains the line through u and the origin.
Answer: True
c) Asking whether the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution amounts to asking whether b is in Span{a1, a2, a3}.
Answer: True
d) If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A.
Answer: True
e) If A is an m × n matrix whose columns do not span R m then the equation Ax = b is inconsistent for some b in R m.
Answer: True
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.