[1 1 31 1 Find eigen value and eigen vector of given matrix 15 1 3 1 1 2 Solve the simultaneous differential equation by using matrix method t = y+2y2; = 5y1 +4y2 t 1 1 1 3 Find eigen value and eigen vector of given matrix 0 2 4 4 3 13 4 Solve the simultaneous differential equation by using matrix method t = 4y1 y2; = 3y1 +2y2 t 7 -2 1 5 Find eigen value and eigen vector of given matrix |-2 10 -2 6 -2 7 Find the eigen values and eigen vectors of the matrix generated by the given system of equations 10x 2y+4z = 0 - -20x+4y-10z = 0 -30x+6y 13z = 0 7 8 -6 2 Prove that for the matrix A = -6 7 -4 all its eigen values are distinct and real. 2 -4 3 Hence find the corresponding eigen vectors.