HW10-510-soln

# HW10-510-soln - AMS 510 HW10 Solution 5.49(a We can easily...

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AMS 510 HW10 Solution 5.49 (a) We can easily verify that if U=(x, y, z), V=(a, b, c), then F(U+V)=F(U)+F(V); and F(kU)=kF(U). (b) same method with (a). 5.50 All of (a), (b), (c) and (d) can't satisfy the criteria that F(kU)=kF(U). 5.52 (a) A = 17 5 23 6 (b)No. 5.54 We can verify that (a), (b) satisfy addition and multiplication rule, so (a), (b) are lineal mapping, but (c) doesn't satisfy addition rule. T A B = M A B M A M B = T A  T B . 5.57 (a) If G x, y , z = x y z, y – 2 z, y – 3 z = a,b,c , then { x y z = a y – 2 z = b y – 3 z = c { x = a 4b 3c y = 3b 2c z = b c , as x 2 y 2 z 2 = 1 a 2 26b 2 14c 2 8ab 6ac 38bc = 1 . (b) If G 1 a,b,c = x, y ,z , then { x y z = a y – 2 z = b y – 3 z = c , as a 2 b 2 c 2 = 1 x 2 3y 2 14z 2 2xy 8yz 2xz = 1 .

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HW10-510-soln - AMS 510 HW10 Solution 5.49(a We can easily...

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