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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Q. A linear transformation from a finite dimensional inner product space V to itself is shew ymmetric if they commatelesA necessary and sufficient condition that a linear transformation P on a complex inner product space V be self adjoint., Prove the both parts , and only handwriting solution , don't copy from other sources
- Apply Gram - Schmidt process to construct an orthonormal for R4 with the standard inner product from the basis (V1, V2, V3) where V, = (1, 1, 1, 1), V2 = (1, 2, 0, 1), V3 = (2, 2, 4, 0).Consider L ∞[−1, 1] with the essential sup-norm (see Definition3.2.12). Show that the essential sup-norm cannot be induced by an inner product.state and prove cauchy schwartz theorem
- Please ASAP , A necessary and sufficient condition that a linear transformation P on a complex inner product space V be self adjoint., Prove the both parts , and only handwriting solution , don't copy from other sourcesFind the Basis of NULL Space of A and also What is the dimension of Nul A?Prove that a finite projective plane of order n has n2 + n + 1 points andn2 + n + 1 lines.
- Show that A and AT have the same nonzero singular values. How are their singular value decompositions related?Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (2x, y).find a basis for null space of A, state nullity, and describe the null space geometrically