Question: Consider the inner product on R 2 given by (a) Let A E 2 (R?) be the operator defined by A(r, y) = (-y, z).

Consider the inner product on R²given by

(a) Let A E 2 (R?) be the operator defined by A(r, y) = (-y, z). Show that A is normal with respect to the dot product on R', but not normal with respect to (-, --). Hint: Show that set { (1, 0), (1, 1) , is an orthonormal basis of R' with respect to (-, -).W1 (v. W # W2

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