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:
20
Step-by-step explanation:
I just took test let me know if I’m wrong but I’m 100 perfect I’m right
Answer:
450m South
Step-by-step explanation:
Total distance traveled Northward :
1000m + 600m = 1600m Northward
Total distance traveled Southward :
1250m + 800m = 2050m
The Displacement :
Southward - Northward
2050m - 1650m
= 450m
Since, it covers more distance towards the south, then, direction is southward
450m South
Answer:
<h2>x² = -3</h2>
Step-by-step explanation:
In algebra, the goal is always to isolate the variable, so its value can be determined.
<h3>Step 1: Subtract 21</h3>
7x² = -21
<h3>Step 2: Divide by 7</h3>
x² = -3
<h3>Step 3: Check</h3>
7(-3) + 21 = 0
0 = 0 ✔
<h3>Step 4: Answer</h3>
x² = -3
I'm always happy to help :)
Answer:
Hope this helps!
Step-by-step explanation:
We will need the loan payment formula:
That formula is really complex and we expect you to solve it.
Your monthly payment would be $1.93 per month for 6 years making the TOTAL loan cost 1.93 * 12 * 6 = 138.96
Since the principal you borrowed is $120 the total interest =
(138.96 minus 120.00) which equals $18.96