what will be the eigen values & eigen vectors of the matrix?

Question

9 -1 -9
3 -1 3
-7 1 -7
please give me answer within a day

Answer 1

_|-1 3|_____|3 3 |_____|3 -1|
9|1 -7| + _-1 |-7 -7|+ __-9 |-7 1|

Its hard to show you here!

Answer 2

I'll show you how to reach an answer.
now, we know that if:
Ax =c*x
That means that c is an eigen value and x is an eigen vector.
Let's develop this:
Ax-cx = 0
(A-cI)x = 0
Because to non-zero matrices can lead to a zero result, this equation gives us nothing. But we can use a determinant on it, to help:
det((A-cI)x) = I'll show you how to reach an answer.
now, we know that if:
Ax =c*x
That means that c is an eigen value and x is an eigen vector.
Let's develop this:
Ax-cx = 0
(A-cI)x = 0
This means that x is non-null solution to the matrix. This can only
happen if:
det(A-cI) = 0

And so we get a polynom. In you case:

|(9-x) -1 - 9 |
|3 (-1-x) 3 | = 0
|-7 1 (-7-x)|

We get a 3rd degree polynom to solve.

Answer 3

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Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).

The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and arises in such common applications as stability analysis, the physics of rotating bodies, and small oscillations of vibrating systems, to name only a few. Each eigenvalue is paired with a corresponding so-called eigenvector (or, in general, a corresponding right eigenvector and a corresponding left eigenvector; there is no analogous distinction between left and right for eigenvalues).

The decomposition of a square matrix A into eigenvalues and eigenvectors is known in this work as eigen decomposition, and the fact that this decomposition is always possible as long as the matrix consisting of the eigenvectors of A is square is known as the eigen decomposition theorem.


In mathematics, an eigenvector (help·info) of a transformation[1] is a non-null vector whose direction is unchanged by that transformation. The factor by which the magnitude is scaled is called the eigenvalue (help·info) of that vector. (See Fig. 1). Often, a transformation is completely described by its eigenvalues and eigenvectors. An eigenspace is a set of eigenvectors with a common eigenvalue.

These concepts play a major role in several branches of both pure and applied mathematics — appearing prominently in linear algebra, functional analysis, and to a lesser extent in nonlinear situations.

It is common to prefix any natural name for the solution with eigen instead of saying eigenvector. For example, eigenfunction if the eigenvector is a function, eigenmode if the eigenvector is a harmonic mode, eigenstate if the eigenvector is a quantum state, and so on (e.g. the eigenface example below). Similarly for the eigenvalue, e.g. eigenfrequency if the eigenvalue is (or determines) a frequency.