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Unformatted text preview: A := 1 2 31 12 0 1 1 and B := 2 1 01 1 1 3 2 1 (a) row equivalent? (b) similar? 4. Show that he formula h f, g i := 1 2 π Z 2 π f ( t ) g ( t ) dt deﬁnes an inner product on C [0 , 2 π ]. Let W := span { 1 , sin t, cos t } . What is the orthogonal projection of t onto W ? 1 5. A linear map T : IP 2 → IP 3 is deﬁned as T : f ( t ) 7→ ( t 2 f ( t )) . Find (a) its matrix representation for the standard bases { 1 , t, t 2 } of IP 2 and { 1 , t, t 2 , t 3 } of IP 3 ; (b) a basis for ker( T ); (c) a basis for range( T ). 6. Given A := ± 1 2 1 0 ² , compute A 1000 . 2...
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 Winter '08
 R.Schmidt
 Linear Algebra, #, student id, necessary steps, Mock midterm test

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