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 = 6x1 - 5x2, x 2 = 4x1 + 2x2 C What is the general solution in matrix form? x(t) =

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

Consider the following linear system y + The coefficient matrix is known to have eigenpairs (1, H) and (-1,): Use the method of variation of parameters to find a particular solution of this non-homogeneous system.

Solve a simple system: 3x + 2y − z = 2x − y + 5z = −22x + y = 3 a. Matrix representation of system linear equation above into a matrix representation in form of Ax = B then find x= = A−1B, which represents x = [x y z] b. Cramer’s rule method to find x, y, and z.

The matrix below is in echelon form. x y 1 8 10 0 0 0 Write the corresponding linear system. equation 1 x + y = equation 2 x + y = Solve the linear system. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t as the parameter. If there is no solution, enter NONE.)(x, y) = ( )

Use an inverse matrix to solve each system of linear equations. (a) x + 2y = -1 x - 2y = 3 (x, y) = = (1 (b) x + 2y = 11 x - 2y = -5 (x, y) = (1