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Question 1 a. During an experiment to prove the effectiveness of a modern control device; a matrix B was obtained. This matrix has the following elements as shown below [3 6-8] B = 006 Lo o 2 Show that, this system with real entries (i.e. in R³x3) has real eigenvalues which are neither non-zero nor non-complex. Major Topic: 5 Eigenvalues b. With the same information, show that the eigenvectors associated to the eigenvalues can be determined Major Topic: 5 Eigenvalues & Eigenvectors Blooms Designation: Score: 7 AP Major Topic: 3 Laplace Transform (in the form Blooms Designation: Score: 7 AP c. Show that the Laplace Transform 2e³t (4cos2t-5sin2t) is in the form entf(t). Blooms Designation: Score: 6 AP