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:
300
Step-by-step explanation:
The answer is 12.8 cm³
<span>The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p):
v = k/p
p * v = k (k - constant)
p1v1 = k
p2v2 = k
So, p1v1 = p2v2
v1 = 24 cm</span>³
p1 = 16 lb
v2 = ?
p2 = 30 lb
24 * 16 = x * 30
384 = x * 30
x = 384 / 30
x = 12.8 cm³
