1. Determine the matrix function et in the following cases: 10 01 0 1 4- (1...

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1. Determine the matrix function et in the following cases: 10 01 0 1 4- (1 9). ^- (8 5)- ^- (-98) A = A= A = 2. Determine the general solution of the system y₁ = 6y₁ - 3y2 y₂ = -2y₁ + y2 3. Determine a fundamental matrix of the vectorial ODE 1 y (t) = ( 3 4 ) 3 (1) 32 4. Determine the solution of the initial value problem 3' (1) – († 1 ) v(0), 4(0) = 5. Determine the solution of the initial value problem 1 J(0) = (1 = ( 4 -¹2 ) y(t), y(0) = 12 ( 1 ) 6. Determine the solution of the initial value problem 1 -5 y (t) = ( = ( ₂ − 5 ) v(t), y(0) = ( 2 -5 -(i) 7. Determine a real-valued basis of the solution space of the vectorial ODE 1 y' (t) = (- - ( - 2 -1)v(t) -2 Compute A and e 8. A vectorial ODE of the form y'(t) = Ay(t) has a fundamental matrix Y(1) = (3 4e6t elit (1) et 1. Determine the matrix function et in the following cases: 10 01 0 1 4- (1 9). ^- (8 5)- ^- (-98) A = A= A = 2. Determine the general solution of the system y₁ = 6y₁ - 3y2 y₂ = -2y₁ + y2 3. Determine a fundamental matrix of the vectorial ODE 1 y (t) = ( 3 4 ) 3 (1) 32 4. Determine the solution of the initial value problem 3' (1) – († 1 ) v(0), 4(0) = 5. Determine the solution of the initial value problem 1 J(0) = (1 = ( 4 -¹2 ) y(t), y(0) = 12 ( 1 ) 6. Determine the solution of the initial value problem 1 -5 y (t) = ( = ( ₂ − 5 ) v(t), y(0) = ( 2 -5 -(i) 7. Determine a real-valued basis of the solution space of the vectorial ODE 1 y' (t) = (- - ( - 2 -1)v(t) -2 Compute A and e 8. A vectorial ODE of the form y'(t) = Ay(t) has a fundamental matrix Y(1) = (3 4e6t elit (1) et