Consider the matrices:
Find elementary matrices E1, E2, E3, and E4 such that
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(a)
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.
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(b)
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.
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(c)
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.
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(d)
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.
Let
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(a)
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Find the lengths of and , and compute the dot product .
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(b)
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Find the angle between and . Are and orthogonal?
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(c)
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Find the projection of onto .
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(d)
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Find the projection of onto .