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Example Question #1 : Eigenvalues And Eigenvectors
Find the Eigen Values for Matrix .
There are no Eigen Values
The first step into solving for eigenvalues, is adding in a along the main diagonal.
Now the next step to take the determinant.
Now lets FOIL, and solve for .
Now lets use the quadratic equation to solve for .
So our eigen values are
Example Question #2 : Eigenvalues And Eigenvectors
Find the eigenvalues for the matrix
The eigenvalues, , for the matrix are values for which the determinant of
is equal to zero. First, find the determinant:
Now set the determinant equal to zero and solve this quadratic:
this can be factored:
The eigenvalues are 5 and 1.
Example Question #381 : Operations And Properties
Which is an eigenvector for ,
or
both and
neither one is an Eigenvector
To determine if something is an eignevector, multiply times A:
Since this is equivalent to ,
is an eigenvector (and 5 is an eigenvalue).
This cannot be re-written as times a scalar, so this is not an eigenvector.
Example Question #1 : Eigenvalues And Eigenvectors
Find the eigenvalues for the matrix
The eigenvalues are scalar quantities, , where the determinant of
is equal to zero.
First, find an expression for the determinant:
Now set this equal to zero, and solve:
this can be factored (or solved in another way)
The eigenvalues are -5 and 3.
Example Question #5 : Eigenvalues And Eigenvectors
Which is an eigenvector for ,
or
?
Both and
Neither is an eigenvector
Both and
To determine if something is an eigenvector, multiply by the matrix A:
This is equivalent to so this is an eigenvector.
This is equivalent to so this is also an eigenvector.
Example Question #6 : Eigenvalues And Eigenvectors
Determine the eigenvalues for the matrix
The eigenvalues are scalar quantities where the determinant of
is equal to zero. First, write an expression for the determinant:
this can be solved by factoring:
The solutions are -2 and -7
Example Question #7 : Eigenvalues And Eigenvectors
Which is an eigenvector for the matrix ,
or
Both and
Neither one is an eigenvector
To determine if a vector is an eigenvector, multiply with A:
. This cannot be expressed as an integer times
, so
is not an eigenvector
This can be expressed as
, so
is an eigenvector.
Example Question #8 : Eigenvalues And Eigenvectors
Example Question #1 : Eigenvalues And Eigenvectors
Example Question #10 : Eigenvalues And Eigenvectors
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