Answer:
dim L = dim U = 
Step-by-step explanation:
We can do it only for the lower-triangular matrices, the case of the upper-triangular matrices is similar. We might caracterice nxn the lower-triangular matrices, as the nxn matrices 
such that the entry 
if i<j.
Now let and 
be two lower triangular matrices, now if
for some 
then the entry 
of C is equal to
Now, if i<j, it must hold that 
. Therefore, if this is the case we must have that 
and so we get that C is also a lower triangular matrix. This showa that L is closed under sum and scalar multiplcation, hence it is a linear subspace.
To find the dimension, note that all the entries of a lower-triangular matrix over the diagonal must be equal to zero. However, each entry of the matrix under the diagonal and in the diagonal might be any element of 
, any entry that can be choosen add up to the dimension of L, we n such elemnts for the first column, (n-1) for the second column, (n-2) for the third column etc.... Therefore,
Answer:
then simply become a french fry lol
Step-by-step explanation:
