bhuvaneshnick
Junior Member
- Joined
- Dec 18, 2014
- Messages
- 55
Since when does the b-column "have" to be all zeroes in order for there to be a solution to the system of equations? (Think back to the systems you've solved by hand.)A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence for this system is:
a) A must be invertible.
b) b must be linearly dependent on the columns of A.
c) b must be linearly independent of the columns of A.
d) None of these.
B column must be linearly dependent with A so only we can make the B column zero to further move to find solution of the system.am i thinking right?
Since when does the b-column "have" to be all zeroes in order for there to be a solution to the system of equations? (Think back to the systems you've solved by hand.)
If you're working with the matrix equation, what would you multiply by (on the left) in order to get x by itself, with the solution vector on the other side of the equation? What must be true in order for that multiplication to be able to take place?![]()
The "rule of elementary matrix operations" is to get to "echelon form" or "reduced echelon form", it does not have any thing to do with whether or not the columns, thought of as vectors, are dependent or independent.For multiplication to take place B should be dependent
okay we get to that question later, before that i have few question,let A be matrix of
1 0
3 0
1)now say are the column vectors dependant or not? what i was thinking is multiplying anything with column 1 dont make the column 2, isn't it .so the vectors are independent right? .though we multiply zero,but rule of elementary matrix operation is only about non zero multiplication