# Laplace transform

Name Math 264 Summer 2021 Homework Set 5 Show all work! 1. Find the Laplace transform of f (t) = 4t 3 6 cos 3t + e 2. Find the inverse Laplace transform of F (s) = 1 8 s +2 + 7t . (3 pts.) 2s 18 2 s + 36 . (3 pts.) 3. Solve the IVP using the Laplace transform. y 00 0 8y + 15y = e 4t ; y(0) = 2; 0 y (0) = 0 (6 pts.) 2 4. Suppose that A = and B = (a) Evaluate 4A + 3B. (b) Evaluate (BA) T. 4 2 7 8 6 3 1 5 (1 pt.) (1 pt.) 5. Let A be an augmented matrix for a system of three linear equations in three unknowns. Suppose that B = 0 @ 1 0 4 0 0 1 2 0 0 0 0 1 1 A is the reduced row-echelon form of A. Is there a solution to the system of equations? If so, what is the solution set? Justify your answer. 3 (2 pts.) 6. Use Gauss-Jordan reduction to solve the system consisting of the following equations. (4 pts.) x + 2y + 3z = 5; 2x 4y 4 2z = 2; 3x 2y + 2z = 11

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