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HW3SolutionsF07 - 4.38 4.39 4.40 4.42 The phase and...

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4.38 4.39 4.40
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4.42
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The phase and magnitude plots obtained are as shown: 5.10
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5.11
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C1 = [ 1 5 6] C2 = Not possible. Matrix dimensions do not agree. Atranspose= [1 -1 3 0 2 1 1 0 1] C3= [-2 6 1] C4 = Matrix dimensions do not agree. 5.12
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5.20
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5.22
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6.1 1. non-linear, circle 2.non-linear, sphere 3.linear, y-axis 4.non-linear, ellipse 5.non-linear 6.linear, straight line through origin with slope=45 deg.
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6.2 6.3
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6.4 The number of equations is 6, and the number of variables is 8. Thus an undetermined system can be written as: x 1 + x 2+ x 3+ x 4+ x 5+ 3x 6+ x 7+ x 8 =10 2x 1 + x 2+ 5x 3+ 6x 4+ 6x 5+ 7x 6+ x 7+ 9x 8 =15 x 1 + 13x 2+ 14x 3+ 5x 4+ 6x 5+ 4x 6+ 9x 7 =13 9x 1 + 6x 2+ x 3+ x 4+ x 5+ 32x 6+ 5x 7+ 3x 8 =40 x 1 + 4x 3+ 5x 4+ 6x 5+ 8x 6+ 4x 7+ 7x 8 =8 10x 1 + 11x 3+ 4x 4+ 2x 5+ 3x 6+ 2x 7+ 8x 8 =0
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6.5 Take m=3, n=2 X 1 - X 2 =2 X 1 + 3X 2 =6 X 1 + X 2 =4 6.6 Take m=3, n=2 X 1 - 2X 2 =1 3X 1 + 3X 2 =7 2X 1 + 5X 2 =4 6.7 X 1 + X 2 + X 3 =5. X 1 + 2X 2 + 2X 3 =10.
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6.8 6.18. Augmented matrix = [1 1 1 6 0 1 2 4 0 1 1 3] R1 R1-R3 [10 0 3 0 1 2 4 0 1 1 3] R3 R3-R2 [1 0 0 3 0 1 2 4 0 0 -1 -1] R3 R3*-1 [1 0 0 3
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0 1 2 4 0 0 1 1] R2 R2-2*R3 [1 0 0 3 0 1 0 2 0 0 1 1] Thus, [x1 [3 X2 = 2 X3] 1] 6.19
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6.20 Augmented matrix becomes: [ 1 0 1 1 0 2 a 2
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