Consider the matrix equation AX-B where: A = e^t cos(t) sin(t) e^t - sin(t) cos(t) e^t-cos(t)-sin(t)...

 

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Consider the matrix equation AX-B where: A = e^t cos(t) sin(t) e^t - sin(t) cos(t) e^t-cos(t)-sin(t) B = 0 2 0 a) Calculate det(A) and show that det(A) is not equal to 0 for all. b) Using Cramer's Rule identify the matrices A1,A2 and A3 for the matrix equation AX-B c) Calculate det(A1),det(A2) and det(A3) d) Use Cramer's Rule to find a solution to AX-B in terms of t e) Is there any value of t for which the solution to AX-B is the trivial solution? Justify your answer. Consider the matrix equation AX-B where: A = e^t cos(t) sin(t) e^t - sin(t) cos(t) e^t-cos(t)-sin(t) B = 0 2 0 a) Calculate det(A) and show that det(A) is not equal to 0 for all. b) Using Cramer's Rule identify the matrices A1,A2 and A3 for the matrix equation AX-B c) Calculate det(A1),det(A2) and det(A3) d) Use Cramer's Rule to find a solution to AX-B in terms of t e) Is there any value of t for which the solution to AX-B is the trivial solution? Justify your answer.