- #1
lax1113
- 179
- 0
Homework Statement
Given the following conditions, determine if there are no solutions, a unique solution, or infinite solutions. (Matrix A|B = augmented matrix).
Just in case anyone viewing needs a little refresher... Rank = number of non zero rows in the matrix.
1)
# of equations : 3
# of unknowns : 4
Rank of Matrix A : -
Rank of Matrix A|B: 2
2)
# of equations : 4
# of unknowns : 4
Rank of Matrix A : 4
Rank of Matrix A|B: -
2. Homework Equations and attempt
So I know that for a system to be consistent, the rank of A has to be equal to the rank of A|B. At this point, if this is true, we can then go on to say that if the rank of A is less than the # of unknowns, then A has infinite solutions (Unknowns - Rank(A) = free parameters). The only thing that I am not sure about is how to determine the Rank of A given the other 3, or the rank of A|B. Is this question asking for multiple answers?
For example, for number one, would I say that in the case that Rank(A) is less than Rank A|B, the system is inconsistent, while if the rank of A is equal to that of A|B then the system is consistent with infinite solutions because A<unknowns? I feel like with the number of given equations I should be able to figure out the missing part, since with the way that I just looked at it I am basically completely ignoring the information given in the equations.
I am really stuck on how to find out the other rank (if it is even possible!) and I have an exam on this tomorrow, so any hint would be greatly appreciated. I couldn't find problems like this online or in my book at .
Thanks