Question
Question1, Determine the values of a for which the system has no solution, exactly 1 solution or infinitely many solutions: x + 2y + z
Question1, Determine the values of a for which the system has no solution, exactly 1 solution or infinitely many solutions:
x + 2y + z = 2
2x 2y + 3z = 1
x + 2y (a^2 3)z = a
Question 2 :Let u1 = (1, 1, 0), u2 = (0, 1, 1), u3 = (1, 0, 1). Find scalars c1, c2, c3 such that c1u1 + c2u2 + c3u3 = (1, 0, 0).
Question 3 :Find the standard matrices for the following 2 linear operators on R 2 : (a) a reflection about the line y = x. (b) a rotation counterclockwise of 30 .
Question 4: Let A = 14 12 20 17 . Find an invertible matrix P and a diagonal matrix D such that D = P 1AP.
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