## Q. 3.12

## Chapter 3

## 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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