Linear Algebra and Its Applications, 4th Edition 4th Edition

companyspends $0.40 on materials, $0.30 on labor, and $0.15 on overhead. For $1.00 worth ofproduct B, the company spends $0.40 on materials, $0.25 on labor, and $0.15 on overhead.Let1)0.400.40a = 0.30 and b = 0.25 .0.150.15Then a and b represent the "costs per dollar of income" for the two products.Evaluate

2 -1 -3 , B =1 6 2 25 3 74 -1 0 3A)C)1)B)-4 -1 32 23-17 -3 14 -121 11 46 52D)-8 0 32 20-5 -6 14 8-7 18 46 31Answer: BExplanation:-4 -1 32 23-17 -3 14 -121 11 46 52-4 -1 0 3-12 -3 0 -928 -7 0

14-2 2 -6 1A) 80Answer: CExplanation:B) -403)-14-3A)4)87-4A)B) 11C) 213D) -35A)B)C)D)3)B) 38C) 14D) 24A)B)C)D)0 0-4 02 2-64Answer: AExplanation:D) -802)2 -13 -2-4 -1-38Answer: BExplanation:C) -160A)B)C)D)4 1 52) 5 4 34 1 4A) -11Answer: AExplanation:1)4)B) 50C) 64A)B)C)D)1D) -784 1 25) -4 -1 -58 5 35)A) 0Answer: CExplanation:B) -12C) 36A)B)C)D)Calculate the area of the

equations in 39variables. The 4 solutions are linearly independent and all other solutions can beconstructed by adding together appropriate multiples of these 4 solutions. Will the systemnecessarily have a solution for every possible choice of constants on the right side of theequation? Explain.1)Answer: No.Let A be the 36 × 39

-4 -41) A = - 414 , = -34 -4 -7A)B)C)D)0101 0110 , 10 , 101 -1-1-1 1-1Answer: BExplanation:A)B)C)D)Find the eigenvalues of A, and find a basis for each eigenspace.2) A = 2 4-4 21 ; 2 + 4i, 1A) 2 - 4i,B) 2 - 4i,i-iC) 2 - 4i, 1

1 1 1 1 0

0 -9 0 1 00 10 5 0 1C)A = -9 0 9 0 1 00 5 0 5 0 1Answer: BExplanation:1)B)D)A = -1 00 19 00 51001A = -9 00 59 00 5-1 00 1A)B)C)D)Find a unit vector at which the quadratic form x TAx is maximized, subject to

precedes it.1121) 1 , 3 , 0 , p =11 5 62A) 2,57,22Answer: BExplanation:B) 1,33,22C) (-9, 3, 7)D)1)33,- ,122A)B)C)D)Provide an appropriate response.2) Suppose {v1 , v2 , v3} is a basis for 3 . Which of the following statements are true?2)I: Span {v2 -v1 , v3 - v1 } is

and q in S, the line segment between p and q lies in S.[This line segment is the set of points of the form (1 - t)p + tq for 0 t 1. ]Let F be the feasible set of all solutions x of a linear programming problem Ax b