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MATH 54 QUIZ 11-
1. Express the given system of differential equations in matrix notation.
x'1 = -2x2 + x1 - 4x3
x'2 = 3x3 + x2 - x1
x'3 = -x1 + 2x3 - 3x2
2. Find a 4 × 4 matrix A with constant coefficients such that x(t) = is a solution to x'(t) = Ax(t).
3. Show that the following collection of vector-valued functions is linearly independent on R:
4. Find a general solution of the system x'(t) = Ax(t), where A =
5. Find the solution to the system x'(t) = x(t) which satisfies x(0) =
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Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.
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