Quiz2_1806_s05 - By recursion or cofactors or otherwise compute the determinant of this 5 by 5 circulant matrix C ⎠⎀ 2 βˆ’ 1 0 βˆ’ 1 ⎒ βŽ₯

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1 2 3 4 5 6 18.06 Professor Strang Quiz 2 April 1, 2005 Grading Your PRINTED name is:
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1( 1 7 p t s . ) If the output vectors from Gram-Schmidt are cos θ sin θ q 1 = and q 2 = sin θ cos θ describ e all possible input vectors
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2( 1 5 p t s . ) If a and b are nonzero vectors in R n , what number x minimizes the squared length ±
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3( 1 7 p t s . ) Find the projection p of the vector b =(1 , 2 , 6) onto the plane x + y + z
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4( 1 7 p t s . ) Find the determinants of A and A 1 and the (1 , 2) entry of A 1 if A = 0010 1100 1213 1317
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Unformatted text preview: By recursion or cofactors or otherwise(!) compute the determinant of this 5 by 5 circulant matrix C : ⎑ ⎀ 2 βˆ’ 1 0 βˆ’ 1 ⎒ βŽ₯ ⎒ βŽ₯ ⎒ βˆ’ 1 2 βˆ’ 1 0 βŽ₯ ⎒ βŽ₯ ⎒ βŽ₯ C = ⎒ 0 βˆ’ 1 2 βˆ’ 1 0 βŽ₯ ⎒ βŽ₯ ⎒ βŽ₯ ⎒ 0 βˆ’ 1 2 βˆ’ 1 βŽ₯ ⎣ ⎦ βˆ’ 1 0 βˆ’ 1 2 6 6 (17 pts.) Suppose P 1 is the projection matrix onto the 1-dimensional subspace spanned by the first column of A . Suppose P 2 is the projection matrix onto the 2Β­ dimensional column space of A . After thinking a little, compute the product P 2 P 1 . ⎑ ⎀ 1 0 ⎒ βŽ₯ ⎒ βŽ₯ ⎒ 2 1 βŽ₯ ⎒ βŽ₯ A = . ⎒ βŽ₯ ⎒ 0 1 βŽ₯ ⎣ ⎦ 1 2 7...
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This note was uploaded on 01/14/2011 for the course EECS 18.06 taught by Professor Strang during the Spring '05 term at University of Michigan.

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Quiz2_1806_s05 - By recursion or cofactors or otherwise compute the determinant of this 5 by 5 circulant matrix C ⎠⎀ 2 βˆ’ 1 0 βˆ’ 1 ⎒ βŽ₯

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