Let A be an n x n matrix and denote by || A||F the Frobenius norm of A. a) Show that ||A||F = ||U A||F for any orthogonal n x n matrix U. (Hint: multipli- cation by orthogonal matrices does not change vector 2-norms.) b) Show that ||4||F = transposing.) ||AV||F_for any orthogonal n x n matrix V. (Hint: use

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A: Now , V=abcd:a,b,c,d ∈IRbe the Vector spaceof 2×2 real matricesendowed with the inner…

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A: First we calculate the basis of V.

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A: Given set V=abcd: a,b,c,d∈R.

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Q: Please provide detailed solution for II part asap to get a upvote

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Q: iii) Give an example of two matrices A, BE M22(C) such that A) A is not similar to B; and B) PA(:) =…

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Q: Let V be the vector space of real 2 × 2 matrices with inner product    (A|B) = tr(BtA).    Let U…

A: Let A∈skewsymm2 and B∈symm2 Then  A,B=trBtA=trAtB , since A,B=B,A=tr-AB=-trBA=-trBtA ,since B∈symm2…

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A: To check v=111 a vector in a span of S=123, 012, -201 or not.

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Q: 6. Show that the set of all 3 x 1 matrices is a vector space. **end**

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A: Your doubt is right, it is a trick question.A vector space must be defined over a field.But, here,…

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A: All the sub parts are explained in details.

Q: '

A: The null space of T is the collection of all polynomials p(x) in the domain of T such that T(p(x)) =…