Apply the eigenvalue method to find a general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. x1 = 4x1-6x21x2 = x1 - 3x2 What is the general solution in matrix form? 11

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Constants: a = 2, b = 3. Answer each of the following for the given matrix and its reducedrow echelon form:

Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of u1, u2, u3, u4, and u5. Then verify your solution. (Enter your answer in terms of u1, u2, u3, u4, and u5.)v = (6, 1, −10, 11, 8 )u1 = (1, 2, −3, 4, −1)u2 = (1, 2, 0, 2, 1)u3 = (0, 1, 1, 1, −4)u4 = (2, 1, −1, 2, 1)u5 = (0, 2, 2, −1, −1)

Describe and compare the solution sets of x1 +5x2 - 2x3 = 0 and x1 + 5x2 - 2x3 = -7. X1 E Describe the solution set, x= x2 of x1 +5x2 - 2x3 = 0 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. X3 (Type an integer or fraction for each matrix element.) OA. X= O B. X=X3 C. X=X2 O D. X= + X3 X1 E x2 of x1 + 5x2 - 2x3 = = -7 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. x3 (Type an integer or fraction for each matrix element.) OA. X= B. X= +X2 Describe the solution set, x = O c. x= O D. X=X2 +X3 +x2 + X3 +X3 Which option best compares the two equations? O A. The solution set of the second equation is a plane perpendicular to the line that is the solution set of the first equation. O B. The solution set of the second equation is a plane parallel to the plane that is the solution set of the first equation. OC. The solution set of the second equation is a plane parallel to...