2025a1 - -1 , x ), (4 pts) b) T : R 2 R 2 given by T ( x, y...

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MATH 2025 Fall 2005 Assignment 1 Due Thursday, September 15, 2005 before the class 1. Determine whether the set of all vectors ( x 1 , x 2 , x 3 , x 4 ) in R 4 satisfying the system of linear equations 2 x 1 + 3 x 2 + 5 x 4 = 0 x 1 + x 2 - 3 x 3 = 0 is a subspace of R 4 or not. Explain. (6 pts) 2. Show that S := { f ∈ C [ a, b ] | f ( a ) = f ( b ) } is a subspace of C [ a, b ] . (5 pts) 3. Write the product (2 χ [0 , 3] - 3 χ [3 , 6] )( χ [0 , 2] + 5 χ [2 , 4] - 7 χ [4 , 6] ) as a linear combination of the indicator functions of intervals. (6 pts) 4. Determine if the following maps are linear or not. Explain. a) T : R 2 R 3 given by T ( x, y ) = ( x + 3 y, 2 xy
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Unformatted text preview: -1 , x ), (4 pts) b) T : R 2 R 2 given by T ( x, y ) = (3 x + 2 y, x-y ), (4 pts) c) T : C ( R ) C ( R ) given by T ( f ) = f 00 + f. (4 pts) 5. Given ~ v 6 = ~ and ~ p in R n , the line through ~ p in the direction of ~ v has the parametric equation ~ x = ~ p + t~ v , t R . Show that a linear transformation T : R n R n maps this line onto another line or onto a single point (a degenerate line ). (5 pts)...
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This note was uploaded on 11/23/2011 for the course MATH 2025 taught by Professor Staff during the Spring '08 term at LSU.

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