Mark each of the following statements true or false:
(a) If

then (u, v) = u1v1 + πu2v2 defines an inner product on R2.
(b) If

Then (u, v) = 4u1v1 - 2u1v2 - 2u2v1 + 4u2v2 defines an inner product on R2.
(c) (A, B) = tr(A) + tr(B) defines an inner product on M22.
(d) If u and v are vectors in an inner product space with ||u|| = 4, ||v|| = ˆš5, and (u, v) = 2, then ||u + v|| = 5.
(e) The sum norm, max norm, and Euclidean norm on Rn are all equal to the absolute value function when n = 1.
(f) If a matrix A is well-conditioned, then cond(A) is small.
(g) If cond(A) is small, then the matrix A is well-conditioned.

Transcribed Image Text:

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