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,
If a car is going 70 mph it will only take 1 hour to get 70 miles
Answer:
41
Step-by-step explanation:
BDA = DBC+CBA
84=5x+3 + 6x-7
Combine like terms
84 = 11x-4
Add 4 to each side
84+4= 11x -4+4
88 =11x
Divide each side by 11
88/11 = 11x/11
8 = x
We want angle ABC
ABC = 6x-7
=6*8 -7
=48-7
=41
Answer:
Step-by-step explanation:
Numbers 1 and 4 are perimeter questions so all you do is add up all the sides and the label is cm. For #2, this is an area problem and the area for a rectangle is length times width, so multiply the 2 together and the label is inches squared. For #3, the volume formula for a cube is side*side*side and the label for this is feet cubed. For #5, the area for a triangle is .5 times the base times the height, and the label is mm-squared. That should help you get all the answers on your wn. Very, very simple.
Answer:
8.25475 m
Step-by-step explanation:
pi*r^3 is the formula for a sphere.
Using this, pi is a nmber (about 3.14) and we only don't know the radius, but we know what it equals.
pi*r^3=1,767.1
First divide by pi, then get ride of the cube by cube rooting both sides.
The cube root of 1767.1/pi (remember to cube root both denominator and numberator!!!) is about 8.25475 m
