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(1 point) Consider the linear system 3-1_3__3]; a. Find the eigenvalues and eigenvectors for the coefficient matrix. Vi = andI AM STRUGGLING HEAVILY ON THIS PROBLEM PLEASE HELP ME WITH THE CORRECT ANSWERS AND NEAT WORK

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(1 point) Consider the linear system 3-1_3__3]; a. Find the eigenvalues and eigenvectors for the coefficient matrix. Vi = and 12 = -- b. Find the real-valued solution to the initial value problem (y 3yı + 2y2, -5yı - 3y2, yı (0) = 5, y2O) = -5. را Use t as the independent variable in your answers. yı(t) = yz(t) =
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2. 3 -S رو کے -3 Let A = 3 2 3 x 2 Then A-XI1=0 gives - 5 -3-2 or, (3-X) (- 3->) -(10) = 0 x² - 9+10 x2 = -1 eigen values areThe given system can be written as 3 2 5-3 NOW (31) 3ti (Cost tisint) (* 3 Cost - sint ti cost ti 3 sint - 5 cost - 1.5 sint

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