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Suppose that is a Banach space over K. A subspace M of is said to be complemented in if there exists a subspace N of such that =M N, that is if , then there exists in M and in N such that , and M N . Prove that each finite dimensional subspace of is complemented in .
Hint: Suppose that M is a finite dimensional subspace of and is a basis for M. Define linear functionals : M K by for in K, k=1,2,...,n. Apply the Hahn-Banach Theorem, and look at the kernels of the linear functionals.
Build a 25- point numerical integration scheme based on 5- point Gaussian quadrature in the x and y directions. Specify the quadrature points and the summation weights.
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Find the value of x using the given system
Every finitely generated sub module is free.
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1. math is a rectangle. dh ht.the area of triangle dht is 8 .the area of triangle aht is 3 .what is the area of
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Suppose that you have student loan of $80,000 with an APR of 7% for 30 years. If you decide to pay off the loan in 20 years instead of 30.
If the cost of a cell phone has decreased 400% during the past 10 years, does that correspond to a cost decrease of four times? Explain your answer as though you were talking to someone who has never taken algebra.
Estimate whether the system is inconsistent or consistent
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