Hi

Can you please help me with just the True/False questions from #4 - 8 please.  Just the answer is good.  Thank you so much!

 

 

Math 636 Assignment 8 - Quiz Component 1. Which of the following statements is true for all 2 × 3 matrices A?
(a) dim Row(A) > dim Col(A).
(b) rank(A) < dim Null(A).
(c) dim Null(A) ≥ 1.
(d) dim Row(A) + dim Col(A) = 2. 1 0 −1 3
2. If the reduced row echelon form of A is R = 0 1 2 0, then a basis for Null(A) is
0 0 0 0 −1
3
−1
3
1
−3 0
1 2
0
2
0
−2
1
0 , , , 0 , (b)
(c)
(d)
(a) 0 0 1 0 1 0 −1 2 3
0
0
0
1
0
1 0
3. Let L : V
a linear mapping, and let B = {~v1 , ~v2 , ~v3 } be a basis for V. If → V be 2 −1 0
[L]B = 1 2 1 and ~x = 3~v1 − ~v2 + 3~v3 , then
1 1 3 7 (a) L(~x) = 4 11 3 (b) L(~x) = −1
3
(c) L(~x) = 7~v1 + 4~v2 + 11~v3
(d) L(~x) = 5~v1 + 4~v2 + 11~v3
For questions 4 - 8, determine if the statement is True or False. You should make sure that
you have a proof of each true statement and a counter example for each false statement.
4. If A is similar to B and B is similar to C, then A is similar to C.
(a) True.
(b) False.
5. If A and B are similar, then dim(Null(A)) = dim(Null(B)).
(a) True.
(b) False. 1 2 6. If A and B are invertible, then AB and BA are similar.
(a) True.
(b) False. 1 0 1 7. If the reduced row echelon form of A is R = 0 0, then 0 is a basis for Col(A). 0
0 0
(a) True.
(b) False.
8. If L : V → V is a linear mapping and B be a basis for V, then Col([L]B ) = Range(L).
(a) True.
(b) False.

Attachments:

• 1492845688-A8Q.pdf