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Algebra Archive: Questions from June 14, 2022

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  Evaluate the following improper integral if possible. Lº 5xe2x dx
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• Prove the following: If A is an invertible matrix then the system of equations 𝑨𝒙=𝒃 It has a unique solution given by x=𝐴^−1𝑏
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• a)In how many ways can a determinant of 4 times 4 be made. Why? b) Prove that
  a) De cuántas maneras se puede realizar un determinante de 4 por 4. Porqué? b) Demuestre que 1 1 1 1 = (a + 3)(a - 1 1 1 1)3.
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• a) Indicate if it has a unique solution, an infinity of solutions or no solution, argue your response. In case of having an infinity of solutions, indicate what is the basis for the solution space. b)
  Obtenga la solución general del sistema X₁2X2 X3 + 3x4 = 0 - -2x1 + 4x2 + 5x35x4 = 3 3x₁6x₂6x3 + 8x4 = 2 a) Indique si tiene una solución única, una infinidad de soluciones o no tiene soluci�
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• Given the function. Find its minimum value subject to the set of constraints that are listed below. Sketch the feasible region in advance and locate the vertices. If the objective function were quadr
  Dada la función: f(x, y) = -10.x+20.y+760 , encuentre su valor mínimo sujeto a el conjunto de restricciones que se enlistan abajo. Bosqueje de antemano la región factible y localice los vértices.
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  Solve for x, y, and z. X = y = Z = xy 2x-y 6 [x2] + ² [²22] - [ 20 (²5-y)] +2 y z 3y -4z 60 6
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• Apply the graphical method to determine the maximum of the following Linear Programming problem: z = f(x,y) = 49 x−8 y where the decision variables are subject to the constraints: R1: 22 x−19 y≤
  Aplique el método gráfico para determinar el máximo del siguiente problema de Programación Lineal: z = f(x,y) = 49 x-8 y donde las variables de decisión están sujetas a las restricciones: R₁:
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  Let T(x, y) = (2x − y, 3y, x + y) and S(x, y, z) = (4x + 2z, x-2y). Find To S(1, -3, 2) = (
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• Find the value of y such that the matrix . belongs to the subspace of the upper triangular matrices 2×2 generated by
  Halle el valor de y de forma que la matriz 1 M = (33) (² 13 pertenezca al subespacio de las matrices triangular superiores 2 × 2 generador por 7 1 8 A = (₁1) × ² = ( ₂₂ ) y B 01 -
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• Let V⊂R3 be the vector space spanned by the vectors ⎛⎝⎜116⎞⎠⎟ and ⎛⎝⎜1−18⎞⎠⎟ and let W⊂R3 be the vector space spanned by the vectors ⎛⎝⎜14−1⎞⎠⎟ and ⎛⎝�
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• Consider the arrays A=(1047),B=(1059),C=(107f) Then the set {A,B,C} is linearly dependent for f equal to:
  Considere las matrices 1 A = = (₁ 4), B = (15) ₁0 = (17) с 9 9 0 7 9 Entonces, el conjunto {A, B, C'} es linealmente dependiente para f igual a:
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• Consider the matrix A given by A=⎛⎝⎜45116817247⎞⎠⎟. Then, the dimension of the subspace W⊂R3 given by W={v⃗ =(x,y,z):Av⃗ =0⃗ } it is:
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• Let B={(3,1,3),(3,0,−3),(−3,18,−3)}. be an ordered basis for R3 and let v⃗ =(12,−49,36)∈R3 . If the coordinates of v⃗ with respect to B are (α,β,γ), we can ensure that α is:
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  y 3 (₂² 3x+2) = (₁00); Find x, y, z and w z 3y - 2w, 10 A) x = 3; y = 12; B) x = 3; y = 6; z = 13; w = 9 z = -7; w=9 C) x = 3; y = 6; D) x = 3; y = 9; = 10; w=0 z = 7; w = -18 A B C D
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