We can write this as:

`((1,1,1),(-2,3,0),(0,-3,6))((I_1),(I_2),(I_3))=((0),(24),(0))`

So we have:

`((I_1),(I_2),(I_3))=((1,1,1),(-2,3,0),(0,-3,6))^-1((0),(24),(0))`

Using a computer algebra system to perform the inverse and multiply by the constant matrix, we get:

`I_1= -6\ "A"`

`I_2= 4\ "A"`

`I_3= 2\ "A"`

We observe that I1 is negative, as expected from the circuit diagram.

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