Midterm2Review[1]

Midterm2Review[1] - from P 2 to P 2 , T(f)=f’-3f....

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MAT211 Review for Midterm 2 Coordinates - Linear spaces - Orthogonality 1 Example (4.1-25) Let W be the space of all polynomials f in P 3 such that f(1)=0. Determine whether the following subspace of P 3 and if so, Fnd its dimension. EXAMPLE (4.2-13) Let T be a transformation from R 2x2 to R 2x2 deFned by T(M)=A.M - M.A where A is the matrix ±ind out whether T is linear. If it is, Fnd kernel, image and nullity and determine whether is an isomorphism. 1 2 0 1 EXAMPLE (4.2-67) ±or which constants k is the linear transformation T(M)=AM-MB an isomorphism if A and B are the matrices 2 3 0 4 3 0 0 k EXAMPLE (4.3-21) ±ind the matrix (with respect to the standard basis) of the transformation T
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Unformatted text preview: from P 2 to P 2 , T(f)=f’-3f. Determine whether is an isomorphism ±ind basis of kernel and image of T. Determine nullity and rank. EXAMPLE(5.1-27 modiFed) ±ind the orthogonal projection of 9e 1 onto the subspace of R 4 spanned by (2,2,10) and (2,2,0,1) EXAMPLE (5.2-39) Find an orthonormal basis u 1 , u 2 , u 3 of R 3 such that • span(u 1 )=span((1,2,3)) • span(u 1 ,u 2 )=span((1,2,3),(1,1,-1)) EXAMPLE (3.4-39) Denote by T the re±exion abou t the line in R 3 spanned by (1,2,3). Find a basis of R 3 such that the matrix of T is diagonal....
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This note was uploaded on 09/14/2011 for the course MAT 211 taught by Professor Movshev during the Spring '08 term at SUNY Stony Brook.

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Midterm2Review[1] - from P 2 to P 2 , T(f)=f’-3f....

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