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:
= 1 1/3 miles or 1. 336 miles
Step-by-step explanation:
if 1 1/4 (5/4)hrs = 1 2/3 (5/3)miles or if 1.25hrs = 1.67miles
1 hr =<u> 1 hr x 5/3miles</u> or 1 hr = <u>1hr x 1.67miles</u>
5/4hrs 1.25hrs
= <u>1 1/3 miles</u> or <u> 1. 336 miles</u>
Answer:
a=(2,8) b=(8,8)
c=(8,2) d=(2,2)
Step-by-step explanation:
P=rt+0.16s
365=20r+0.16(1500)
365=20r+240
125=20r
r=6.25
So Piper makes $6.25 an hour.
Answer:
I don't know
Step-by-step explanation:
I don't understand the point of this probem. It says that she has 35 envelopes best it doen't say how much can fit into each one. Maybe you ftogot some details pls reply in the comments.
