ea1 7th assignment 11-10

# ea1 7th assignment 11-10 - Neal Bhatia EA1 Assignment#7 1#8...

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Neal Bhatia 11/10/07 EA1 Assignment #7 1. #8. 3 rows #10. AB= [1 -7 -2 14] AC= [1 -7 -2 14] Therefore, AB=AC, but B does not equal C as given in the problem. #16. a. False. The answer is the definition of matrix multiplication except that the vectors should not be added; instead they should form a 3x3 matrix. b. True. That is the definition of matrix multiplication. c. False. The order cannot be switched, since matrix multiplication is not commutative. d. False. As shown in theorem 3, part d, the transpose of a product of matrices equals the product of their transposes in the reverse order, not the same order, as given here. e. True. This property of transposing is shown in theorem 3, part b. 2. #4. A -1 = .25*[-8 4 = [ -2 1 -7 3] -7/4 3/4] #6. A -1 = -.2*[-5 -5 = [1 1

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7 8] -1.4 -1.6] X=A -1 b= [ 2 -5] #14. If (B-C)D=0, then a possible solution is if B- C=0, since 0*D=0. Then B=C. 3. #8. Since the matrix given has 4 pivot positions and is 4x4, according to theorem 8, part c, it must be invertible. #14.
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ea1 7th assignment 11-10 - Neal Bhatia EA1 Assignment#7 1#8...

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