This is just simple subtraction, 59.99 - 47.50
The answer is C: 12.49
Answer:
![P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)](https://tex.z-dn.net/?f=%20P%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B2%7D%7B3%7D%26-%5Cfrac%7B2%7D%7B3%7D%26%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B5%7D%7D%260%26%5Cfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%5C%5C-%5Cfrac%7B4%7D%7B3%5Csqrt%7B5%7D%7D%26%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B3%7D%26%5Cfrac%7B2%7D%7B3%5Csqrt%7B5%7D%7D%5Cend%7Barray%7D%5Cright%29)
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
![A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)](https://tex.z-dn.net/?f=%20A%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-9%26-4%262%5C%5C%20-4%26-9%262%5C%5C2%262%26-6%5C%5C%5Cend%7Barray%7D%5Cright%29)
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.
![P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)](https://tex.z-dn.net/?f=%20P%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-2%26-2%261%5C%5C1%260%262%5C%5C-1%261%260%5C%5C%5Cend%7Barray%7D%5Cright%29)
and
![D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)](https://tex.z-dn.net/?f=%20D%3D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D-14%260%260%5C%5C0%26-5%260%5C%5C0%260%26-5%5C%5C%5Cend%7Barray%7D%5Cright%29)
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 constant of proportionality is 1.89
Step-by-step explanation:
2 pounds = $3.78
1 pound = $3.78/2 = $1.89
Cost y is directly proportional to the pound of potato
y = 1.89x
The constant of proportionality is the cost of 1 pound of potato, and it is 1.89
No, a & b are not independent if they're mutually exclusive.
Mutually exclusive means the two events cannot occur simultaneously. So if "a" happens "b" cannot. In contrast, two events are independent if the occurrence of one has no effect on the occurrence of the other.