The area of a parallelogram is 64 m2. If a diagonal divides the parallelogram into 2 triangles, what is the area of 1 of the tri
1 answer:
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Answer:
(a) Yes,
(b) Yes,
Step-by-step explanation:
First, lets understand what are eigenvectors and eigenvalues?
Note: I am using the notation to denote Lambda(A) sign.
is an eigenvector of matrix A with eigenvalue
is also eigenvector of matrix B with eigenvalue
So we can write this in equation form as
So what does this equation say?
When you multiply any vector by A they do change their direction. any vector that is in the same direction as of , then this
is called the eigenvector of
.
is
times the original
. The number
is the eigenvalue of A.
this number is very important and tells us what is happening when we multiply
. Is it shrinking or expanding or reversed or something else?
It tells us everything we need to know!
Bonus:
By the way you can find out the eigenvalue of by using the following equation:
where I is identity matrix of the size of same as A.
Now lets come to the solution!
(a) Show that is an eigenvector of
and find its associated eigenvalue.
The eigenvalues of and
are
and
, then
so,
which means that is also an eigenvector of
and the associated eigenvalues are
(b) Show that is an eigenvector of
and find its associated eigenvalue.
The eigenvalues of and
are
and
, then
so,
which means that is also an eigenvector of
and the associated eigenvalues are
Answer:
Step-by-step explanation:
Completing the square is a process of converting a quadratic equation in standard form into vertex form.
The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.
Factor out the coefficient of the quadratic term,
Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.
Simplify,
The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.