homework2sol.20100208.4b70480ab7cc40.34994098

# homework2sol.20100208.4b70480ab7cc40.34994098 - TAM 412...

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TAM 412, Homework 2, Selected answers Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign [email protected] 3. Recall that det ( AB ) = det A det B , det ( A ) = ( 1) n det A , and det A T = det A . Also, note that Av = λ v for some column matrix v and scalar λ if and only if det ( A λ I ) = 0 . Finally, recall that v = v 1 e 1 + v 2 e 2 + v 3 e 3 = ˜ v 1 ˜ e 1 + ˜ v 2 ˜ e 2 + ˜ v 3 ˜ e 3 implies that H ˜
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Unformatted text preview: ˜ v 1 ˜ v 2 ˜ v 3 ⎞ ⎠ = ⎛ ⎝ v 1 v 2 v 3 ⎞ ⎠ . 4. Since v has the same components relative to T and e T , it follows that the relationship between these two triads is a rotation about an axis parallel to v . 5. (d) This is the angle of rotation between T and e T about the axis parallel to v . 7. 1...
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