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:173/10
Step-by-step explanation:
2. it can't have three because one of them is a right triangle do D doesn't add up. It can't have 0 because an obtuse angle plus a right angle would go over 180 degrees. So, the most it can have is 2 acute for example 90(right angle) 30(acute) and 60 (acute) is a possible answer. Also, a right angle can only have two acute angles since an obtuse angle would put it over 180 which was already stated
0.05 is on the place of hundred and 0.005 is on the place of thousand
Answer:
should be A
Step-by-step explanation:
Translated left by 7
