Example of Linear Combination (Visual)

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Linear Algebra: For the vectors u and v in the plane, express the vectors w1, w2, and w3 as linear combinations. We interpret linear combinations in terms of uv and xy coordinates.
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The questions seems a little garbled. You want to express U and X as linear combinations of P, Q, R.
If E is the matrix of eigenvectors =[PQR], then U = Ev, where v is the column vector of coefficients for the linear combination. v = (abc) means U =aP+bQ+cR.

Thus v = E^{-1} U if we move E to the other side.

MathDoctorBob
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I have question, if you could help me out here. Given a matrix A 3x3 and 2 vectors U(3x1) and X (3x1). The question says, to express the eigenvectors of A as a linear combination of U and X.

Eigenvectors, assume is P, Q and R. So after i got these values, I am confused as to how to express U and X as linear combination of P, Q and R.

What I did is multiplied U with PQnR and equate it X. Please help!!!Thanks


_krish