ok this was confusing me so any help is appreicated.
suppose A is a n by n matrix. show that the rank of A is n only if the AX = 0 has just the trivial solution.
Printable View
ok this was confusing me so any help is appreicated.
suppose A is a n by n matrix. show that the rank of A is n only if the AX = 0 has just the trivial solution.
Meaning A has n linearly independent coloums vectors.Quote:
Originally Posted by buckaroobill
Thus, they form a basis. Thus, a unique representation.
Since expressing the zero coloum is possible trivially it is the only solution for it must be unique.
What do you mean by "linearly independent"?
The coloums of the matrix are linearly independent.Quote:
Originally Posted by buckaroobill
Because Rank(A)=n.