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(30 points) The coordinates of a point in the coordinate system A are given by (3;, y). IV. VI. Find the coordinates (1,5,0) of the same point in coordinate system B in terms of :8, y, and 9. Find a 2x2 u a: matrix RE Such that [ ] 2 RE [ ] . 'U 9 Find the coordinates (z, w) of the same point in coordinate system C in terms of u, v, and q!) Find a 2x2 matrix Rg Such that [ z ] : Rg [a] . w 1; Find the coordinates (2,111) of the same point in coordinate system C in terms of w, y, and 9 + q. Find a 2x2 matrix R3 such that [ z ] = R3 [9:] . w I! Show that RE 2 RgR. For 6 = 30, nd the eigenvalues and the eigenvectors of R3 by solving the characteristic equation. Show all steps. Food for thought: for what values of 6 can RE have a real eigenvector