What is the solution for a matrix with a parameter in its determinant?

[lardycake]

Homework Statement

Hello all,

I have a parameter x of a matrix M = [21, 7
14, 7]
the determinant of
|(M - xI)| = 0

Homework Equations

I is known as the identity matrix

The Attempt at a Solution

My solution seems to be a bit far fetched:

(21 - x)(7-x) - 98 = 0

x2 - 28x + 147 - 98 = 0

x2 - 28x + 49 = 0

using the quadratic formula x = (28 +- root(28x28 - 4(1)(49))) / 2
which I got to be 14 +- 7root(3)

Is this the correct method and answer?

Regards,
Mr Lard

 

[Mark44]

Yes. And what you are calling parameters are usually called eigenvalues of the matrix.