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:
Step-by-step explanation:
The point-slope formula is 
where we substitute a point (x,y) for 
.
We have m=3 and (-1, 2). We input m and 
.
Answer:
I'm pretty sure that the answers would go, Wrong, increased, 9 1/2 points, 6 5/8 points, dropped, 12 3/4 points.
Step-by-step explanation:
The reason why it would be wrong is because the amount of points lost was less than the total amount of points gained.
In week one and two the company gained 9 1/2 points and 6 5/8 points. When you add them together, you get 16 1/8 points.
In week three the company lost 12 3/4 points. If you multiply the fraction to change the denominator to 8, the mixed fraction becomes 12 6/8.
16 1/8 - 12 6/8 = 3 3/8
As you can see, there are still points left over.
In the fourth week, they ended up losing all of their points and then some more, but from my understanding it's just asking about the third week.
Hope that this helps!
Answer:
C
Step-by-step explanation:
16 ounces is equal to 1 pound
Divide 54 by 16 and you get 3.375
You know that there are 3 pounds now, so subtract 3 from what you got to get 0.375
Now multiply 0.375 by 16 to turn it back into ounces, which is 6
3 pounds and 6 ounces is answer choice C
