Q. 3.12

Let $\overrightarrow{a_{1} }=\left(-1,1,1\right), \overrightarrow{a_{2} }=\left(1,-1,1\right)$ and $\overrightarrow{a_{3} }=\left(1,1,-1\right).$

(1) Try to find linear operators mapping the tetrahedron $\Delta \overrightarrow{0}\overrightarrow{a_{1} }\overrightarrow{a_{2} } \overrightarrow{a_{3} }$ onto the tetrahedron $\Delta \overrightarrow{0} \left(-\overrightarrow{a_{1} }\right) \left(-\overrightarrow{a_{2} }\right) \left(-\overrightarrow{a_{3} }\right).$ See Fig. 3.54(a).

(2) Try to find a linear operator mapping the tetrahedron $\Delta \overrightarrow{0}\overrightarrow{a_{1} }\overrightarrow{a_{2} } \overrightarrow{a_{3} }$ onto the parallelogram $\overrightarrow{a_{1} }\overrightarrow{a_{2} }.$ See Fig. 3.54(b).

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