Let 1, 2, 3 be a given positively oriented ON base in space. Define a new...

 

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Let €1, €2, €3 be a given positively oriented ON base in space. Define a new basis f1, f2, f3 by e₁ - e2 + z e3, f2 = ze₁+ ze2 + z e3 f₁ the conditions f3 = − €₁ + €₂ + €3. Show that f1, f2, f3 is also an ON basis. (This reasoning does not need to be submitted). Further calculate the determinant of the transition matrix T. = det(T) = ( ). Is this base positively or negatively oriented? Let €1, €2, €3 be a given positively oriented ON base in space. Define a new basis f1, f2, f3 by e₁ - e2 + z e3, f2 = ze₁+ ze2 + z e3 f₁ the conditions f3 = − €₁ + €₂ + €3. Show that f1, f2, f3 is also an ON basis. (This reasoning does not need to be submitted). Further calculate the determinant of the transition matrix T. = det(T) = ( ). Is this base positively or negatively oriented?

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To show that the basis f1 f2 f3 is an orthonormal ON basis we need to verify two conditions Orthogon... View the full answer