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Suppose that [tex]A \in \mathbb{R}^{3 \times 3}[/tex] who maps the unit sphere in [tex]\mathbb{R}^3[/tex] to an ellips with the following semi-axes;

[tex]x = \left(-\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}},0\right)^{T} \mapsto Ax = (2,0,0)^{T}[/tex]

[tex]x=\left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}},0\right)^{T} \mapsto Ax = (0,-3,0)^{T}[/tex]

[tex]x=(0,0,1)^{T} \mapsto Ax = (0,0,6)^{T}[/tex]

What is the singular value decomposition of [tex]A[/tex]? I'm not allowed to calculate [tex]A[/tex].

Thanks in advance!