Question 6.4.24: What number b in [ 2 b 1 0 ] makes A = QΛQ^T possible? What ...

What number b in \begin{bmatrix} 2 & b \\ 1 & 0 \end{bmatrix} makes A = Q\wedge {Q}^{T} possible? What number makes A = S\wedge {S}^{-1} impossible? What number makes {A}^{-1} impossible?

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Symmetry gives Q\wedge {Q}^{T} if b = 1;

repeated \lambda and no S if b = -1;

singular if b = 0.

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