Question

find eigen values eigen vector for

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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

For a square matrix A, an Eigenvector and Eigenvalue make this equation true:

A times x = lambda times x

We will see how to find them (if they can be found) soon, but first let us see one in action:

Example: For this matrix

−6

3

4

5

an eigenvector is:

1

4

with a matching eigenvalue of 6

Let's do some matrix multiplies to see what we get.

Av gives us:

−6

3

4

5

1

4

=

−6×1+3×4

4×1+5×4

=

6

24

λv gives us :

6

1

4

=

6

24

Yes they are equal! So Av = λv as promised.

Notice how we multiply a matrix by a vector and get the same result as when we multiply a scalar (just a number) by that vector.