So this book has:
If f is a linear transformation, and f(1,0) = (a,c) and f(0,1) = (b,d)
Then the matrix of f is:
a b
c d
What i do not understand is what it means by f(1,0) = (a,c) and f(0,1) = (b,d). So position x becomes a,c but say x was 5 - it tells me little on the logic of how it becomes a and c. The syntax is a bit unusual as it's not entirely clear how it maps.
Can some one clarify this in a more clear way so i understand what it is trying to tell me please.
Currently my guess is, if i had a point (3,2), the matrix becomes:
3 0
0 2
But then b and c are always 0 so that seems a bit redundant in the rule. Hope some one can clear my confusion on this or perhaps has a cleaner way to write the rule so i just change it in a more understandable way.
Thanks
If f is a linear transformation, and f(1,0) = (a,c) and f(0,1) = (b,d)
Then the matrix of f is:
a b
c d
What i do not understand is what it means by f(1,0) = (a,c) and f(0,1) = (b,d). So position x becomes a,c but say x was 5 - it tells me little on the logic of how it becomes a and c. The syntax is a bit unusual as it's not entirely clear how it maps.
Can some one clarify this in a more clear way so i understand what it is trying to tell me please.
Currently my guess is, if i had a point (3,2), the matrix becomes:
3 0
0 2
But then b and c are always 0 so that seems a bit redundant in the rule. Hope some one can clear my confusion on this or perhaps has a cleaner way to write the rule so i just change it in a more understandable way.
Thanks