SOLUTION: For each of the following choices of A and b, determine if b is in the column space of A and state whether the system Ax=b is consistent. A=[1 2] b=[4] [2 4] [8] also

Question 56646This question is from textbook Linear Algebra with Applications
: For each of the following choices of A and b, determine if b is in the column space of A and state whether the system Ax=b is consistent.
A=[1 2] b=[4]
[2 4] [8]
also
A=[1 1 2] b=[1]
[1 1 2] [2]
[1 1 2] [3] This question is from textbook Linear Algebra with Applications

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
For each of the following choices of A and b, determine if b is in the column space of A and state whether the system Ax=b is consistent.
A=[1 2] b=[4]
[2 4] [8]
CHECK THE RATIOS OF ELEMENTS IN THE 2 ROWS UNDER RESPECTIVE COLUMNS ARE EQUAL OR NOT...WE HAVE
1/2,2/4,4/8....ALL ARE EQUAL TO 1/2 .SO THE SYSTEM AX=B IS CONSISTENT
also
A=[1 1 2] b=[1]
[1 1 2] [2]
[1 1 2] [3]
WE HAVE
1/1,1/1,2/2,1/2....THEY ARE NOT ALL EQUAL.
1/1,1/2,2/2,1/3....THEY ARE NOT ALL EQUAL.
HENCE THE SYSTEM AX=B IS INCONSISTENT
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