Consider L[-1, 1] with the essential sup-norm (see Definition Question 1. 3.2.12). Show that the essential sup-norm cannot be induced by an inner product.

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Q: Find a basis for span(l - x, x - x2, 1 - x2, 1 - 2x + x2) in P 2

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Q: If A+ iB is Hermitian (A and Bare real) show that [ AB -BA] is symmetric.

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Q: 2. List all possible Jordan Canonical Form of A if the characteristic poly- nomial is given by (1 –…

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Q: True or False: (p, q) = p(1)q(1)+p(2)q(2) +p(3)q(3) defines an inner product on P2(R).

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Q: (c) 0 is neither diagonalizable nor

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Q: Let α be a zero of x3 + x2 + 1 in some extension field of Z2. Solve the equation (α + 1) x + α = α2…

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Q: Write down 2 polynomials of degree 3 in Q[r] that are irreducible by Eisenstein's criteria.

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