Verify that the vector X is a solution of the given system. dx dt = 3x − 5y dy dt = 5x − 7y; X = 1 1 e−2t Writing the system in the form X' = AX for some coefficient matrix A, one obtains the following. X' = X For X = 1 1 e−2t, one has X' = AX = . Since the above expressions , X = 1 1 e−2t is a solution of the given system.

X is a solution of the system.

Step-by-step explanation:

To verify that the vector X is a solution of the given system:

Writing the system in the form X'=AX for some coefficient matrix A, one obtains the following.

Similarly:

Since the above expressions are equal, is a solution of the given system.

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step-by-step explanation: