Let T R 2 R 2 be given by T(a, b) (b a, a 2b) Show that T is symmetric if the dot product is used in R 2 but that it is not symmetric if the following inner product is used 1 1 (x, y) xAy , A 1 2

Question: Let T: R 2 R 2 be given by T(a, b) = (b a, a + 2b). Show that T is symmetric if the dot

Let T: R²†’ R²be given by T(a, b) = (b €“ a, a + 2b). Show that T is symmetric if the dot product is used in R²but that it is not symmetric if the following inner product is used:

1 -1 (x, y) = xAy

1 -1 (x, y) = xAy", A =_ -1 2.

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