Label the following statements as true or false. (a) The Gram–Schmidt orthogonalization process allows us to construct an orthonormal set from an arbitrary set of vectors. (b) Every nonzero finite-dimensional inner product space has an orthonormal basis. (c) The orthogonal complement of any set is a subspace. (d) If {v1, v2, . . . , vn} is a basis for an inner product space V, then for any x ∈V the scalars <x, v >are the Fourier coefficients of x. (e) An orthonormal basis must be an ordered basis. (f) Every orthogonal set is linearly independent. (g) Every orthonormal set is linearly independent.

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A: GRAM-SCHMIDT METHOD The Gram-Schmidt process (or procedure) is a sequence of operations that allow…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.