# Linear Algebra : Invertible Matrices

Let A be the real 2x2 matrix

[a b]

[c d]

with bc greater than or equal to 0. Prove there exists a real 2x2 invertible matrix S so that S^-1 A S is either diagonal or of the form

[x 1]

[0 x]

where x is the eigenvalue of A.

https://brainmass.com/math/linear-algebra/linear-algebra-invertible-matrices-30857

#### Solution Preview

Please see the attachment.

,

First, we set . We consider the following cases.

1. . Without loss of generality, we can assume . Let . Since . If , then has two distinct zero points and . If , then we note , , . According to the ...

#### Solution Summary

The link between invertibility of matrices and eigenvalues is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.

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