A = [3 2], find all eigen values and eigen vectors of A and hence determine...
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A = [3 2₁], find all eigen values and eigen vectors of A and hence determine =[²₁] for an orthogonal matrix P. 2. Use the Gauss' method to determine the general solution set of the system. Leave your answer in as a vector containing both the particular and homogeneous forms. 1. If A P-¹AP A = 2x + y y x -z 6 3. Find the inverse of the matrix A = -4 - W = 1 +w+u = 6 + 2w = 0 1 1 -1 -2 1 0 1 4. Solve the following system of equations using LU Decomposition method. x¹ + X₂ + X3 = 1 4x₁ + 3x2 - X3 = 6 3x₁ + 5x2 + 3x3 = 4 5. Show that the vectors U₁ = (1,1,1), U₂ = (1,2,3), U¸ = (1,5,8) span R³ - 6. Find the basis and dimension for the solution space of X₁ + X₂ - x3 + 2x4 = 0 X2 X3 X4 = 0 3x₁ + 4x2 - 2x3 + 5x4 = 0 7. Show that f₁ = 1, f₂ = ex and f3 = e2x form a linearly independent set of vectors in C² (-∞0,00). A = [3 2₁], find all eigen values and eigen vectors of A and hence determine =[²₁] for an orthogonal matrix P. 2. Use the Gauss' method to determine the general solution set of the system. Leave your answer in as a vector containing both the particular and homogeneous forms. 1. If A P-¹AP A = 2x + y y x -z 6 3. Find the inverse of the matrix A = -4 - W = 1 +w+u = 6 + 2w = 0 1 1 -1 -2 1 0 1 4. Solve the following system of equations using LU Decomposition method. x¹ + X₂ + X3 = 1 4x₁ + 3x2 - X3 = 6 3x₁ + 5x2 + 3x3 = 4 5. Show that the vectors U₁ = (1,1,1), U₂ = (1,2,3), U¸ = (1,5,8) span R³ - 6. Find the basis and dimension for the solution space of X₁ + X₂ - x3 + 2x4 = 0 X2 X3 X4 = 0 3x₁ + 4x2 - 2x3 + 5x4 = 0 7. Show that f₁ = 1, f₂ = ex and f3 = e2x form a linearly independent set of vectors in C² (-∞0,00).
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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