Answer:
Step-by-step explanation:
It is a result that a matrix 
is orthogonally diagonalizable if and only if is a symmetric matrix. According with the data you provided the matrix should be
We know that its eigenvalues are 
, where 
has multiplicity two.
So if we calculate the corresponding eigenspaces for each eigenvalue we have
,
.
With this in mind we can form the matrices 
that diagonalizes the matrix so.
and
Observe that the rows of 
are the eigenvectors corresponding to the eigen values.
Now you only need to normalize each row of dividing by its norm, as a row vector.
The matrix you have to obtain is the matrix shown below
Answer:
The students went on vacation for average 40 days.
The high school students went for more days than college students.
Step-by-step explanation:
The data shows number of students who went for vacation. The data class frequency shows that students who are in high school went for more days in vacation than college students. The students went for average of 40 days on vacation.
Answer:
195.25
Step-by-step explanation:
Consider geometric series S(n) where initial term is a
So S(n)=a+ar^1+...ar^n
Factor out a
S(n)=a(1+r+r^2...+r^n)
Multiply by r
S(n)r=a(r+r^2+r^3...+r^n+r^n+1)
Subtract S(n) from S(n)r
Note that only 1 and rn^1 remain.
S(n)r-S(n)=a(r^n+1 -1)
Factor out S(n)
S(n)(r-1)=a(r^n+1 -1)
The formula now shows S(n)=a(r^n+1 -1)/(r-1)
Now use the formula for the problem
Answer:
Step-by-step explanation:
The original price of the jacket at the store is $50.
Evan has a coupon for 15$ off. This means that the amount that Evans will pay is the original price - 15% of the original price. It becomes
50 - (15/100 × 50) = 50 - 7.5 = $42.5
Max pays only 0.6 of the price because his father works at the store.
This means that the amount that Max will pay is 0.6 × the original price. It becomes
0.6 × 50 = $30
Max will pay the least amount because his amount is smaller
Answer:
is it 4.8, I don't really know
