Fillable bilinear forms exams online

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SECTION A 1. Let f be the bilinear form on R2 defined by f (x1 , y1 ), (x2 , y2 ) -2x1 x2 + x1 y2 - y1 x2 + y1 y2 . Let u1 (1, 3), u2 (-1, 2). Compute f (u1 , u1 ), f (u1 , u2 ), f (u2 , u1 ), f (u2 , u2 ). Find the matrix A of f relative to the basis u1 , u2 . Find the matrix B of f relative to the basis v1 , v2 , where v1 (-2, -1), v2 (3, 4). Find the change of basis matrix P from u1 , u2 to v1 , v2 and check...
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