HW 8(1)

HW 8(1) - MATH 225 HOMEWORK 8 pp. 351 353 #2, 4 7, 13 19...

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MATH 225 HOMEWORK 8 pp. 351 – 353 #2, 4 – 7, 13 – 19 (odd), 23, 24 – 27, 32 (for all, use the standard bases) pp. 368 – 369 #1 – 6 (ignore geometric description), 12, 14 – 16 A. From problem 12 on page 249, V = ((0, + ), R , #, ) is a vector space over R with a # b = ab for any a, b R , and c a = a c for a (0, + ) and c R . Show that ln( x ) : V R is a linear transformation. B. Recall that for functions f : A B and g : B C , the composition g f : A C is given by g f ( a ) = g ( f ( a )). If T : V F W F and S : W F U F are linear transformations, show that S T is a linear transformation. C. Let S , T : R 1 x 3 R 1 x 3 be the linear transformations given by: T ([ x , y , z ]) = [ y + z , x + z , x + y ] and S ([ x , y , z ]) = [ –z , x z , y + z ]. Find a similar description of the composition S T . If B = { ε i T } is the standard basis of R 1 x 3 , find the matrices [ S ] B and [ T ] B , and show that [
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This note was uploaded on 12/16/2011 for the course MATH 225 at USC.

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