2009asol1 - M346 First Midterm Exam Solutions, February 11,...

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Unformatted text preview: M346 First Midterm Exam Solutions, February 11, 2009 1a) In R 3 , let E be the standard basis and let B = 1 2 3 , 1 4 , 1 be an alternate basis. Let v = 3- 2 14 . Find P EB , P BE and [ v ] B . P EB = ( b 1 b 2 b 3 ) = 1 2 1 3 4 1 , P BE = P- 1 EB = 1- 2 1 5- 4 1 , and [ v ] B = P BE v = 3- 8 37 . 1b) In R 2 [ t ], let E = { 1 , t, t 2 } be the standard basis and let B = { 1 + 2 t + 3 t 2 , t + 4 t 2 , t 2 } be an alternate basis, and let v = 3- 2 t + 14 t 2 . Find P EB , P BE and [ v ] B . This is essentially the same problem as 1a, and has the exact same an- swers. 2. Let L : R 3 R 4 be given by L x 1 x 2 x 3 = x 1 + x 2 + x 3 x 1 + 2 x 2 + 3 x 3 x 1 + 3 x 2 + 5 x 3 x 1 + 4 x 2 + 7 x 3 ....
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2009asol1 - M346 First Midterm Exam Solutions, February 11,...

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