Find a fundamental matrix solution for the system x 0 1 7x1 + 4x2 + 12x3, x 0 2 x1 + 2x2 + x3, x 0 3 −3x1 − 2x2 − 5x3. Then find the solution that satisfies x®(0) h 0 1 −2 i .

Here is the correct format for the question.

. Then find the solution that satisfies  

Step-by-step explanation:

From the figures given above:

the matrix can be computed as,

The first thing we need to carry out is to determine the eigenvalues of A,

where:

the eigenvalues are r = 0, 1, 3

However, the eigenvector correlated to each eigenvalue can be calculated as follows.

suppose  r = 0

(A - rI) x = 0

now the eigenvector is

However, for eigenvalue = 1, we have :  

for eigenvalue = 3, we have:

The solution now can be computed as :

Similarly, the fundamental matrix solution is:

Solving the above equation, we get:

1.8 or

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