Ive tried part b a few times and havent been able to get the

I\'ve tried part b a few times and haven\'t been able to get the correct answer. Any help would be greatly appreciated! Thank you!

Let A be a nonzero 3 × 6 matrix. (a) What is the maximum rank that A can have? 3 (b) If rank(A|B) = 2, then for what value(s) of rank(A) is the system AX-B, B # 0, inconsistent? (Enter your answers as a comma-separated list.) 1,3, 4 x For what value(s) of rank(A) is the system consistent? (Enter your answers as a comma-separated list.) (c) If rank(A) = 2, then how many parameters does the solution of the system AX = 0 have? 4

Solution

In part is given

Rank of [A|B] is 2

So AX= B exists if

Rank of A is also same rank of

[A|B]

i. e rank of A is 2

Since Rank of [A|B]= Rank of A

Then the system is consistent