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(3) Let W be the set of all 22 symmetric matrices. (a) Show that W is the subspace of M22 (the set of all 22

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(3) Let W be the set of all 22 symmetric matrices. (a) Show that W is the subspace of M22 (the set of all 22 matrices). Hint (Check "Subspace Test" section in the following Website). (b) Identify the basis for W. (Hint: A basis is a collection of vectors/matrices that span the set and are linearly independent). 1 (c) What is the dimension of W ? (d) Consider the following matrix: A=(1554) in the subspace W. - Calculate the transpose of A. - Calculate the inverse of A. - Calculate the determinant of A. - Calculate the rank of A

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