- #1

songoku

- 2,302

- 325

- Homework Statement
- Please see below

- Relevant Equations
- det (A - Iλ) = 0

My attempt:

$$

\begin{vmatrix}

1-\lambda & b\\

b & a-\lambda

\end{vmatrix}

=0$$

$$(1-\lambda)(a-\lambda)-b^2=0$$

$$a-\lambda-a\lambda+\lambda^2-b^2=0$$

$$\lambda^2+(-1-a)\lambda +a-b^2=0$$

The value of ##\lambda## will be positive if D < 0, so

$$(-1-a)^2-4(a-b^2)<0$$

$$1+2a+a^2-4a+4b^2<0$$

$$a^2-2a+1+4b^2<0$$

$$(a-1)^2+4b^2<0$$

But the LHS of the inequality is always positive so it is not possible for ##(a-1)^2+4b^2## to be less than 0

Where is my mistake? Thanks

Edit: I just realised my mistake. I will revise my working on post #2