Give an example of a symmetric 3 x 3 matrix A such that: the corresponding...

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Give an example of a symmetric 3 x 3 matrix A such that: • the corresponding quadratic form Q(z) = A is negative semi-definite and has no cross product terms; • the range of the corresponding linear transformation T(7) = Az is 2-dimensional; and • one of the eigenvalues of A has algebraic multiplicity equal to 2. A Find the minimum value of Q(z) = 4, on the unit sphere in R³. Supplementary Problems - Ch. 7 and Google PageRank. Your initials: You do not need to justify your reasoning for questions on this page. 4. Let A = UEV, where Σ= U √60 0 020 000 00 0 [10-1 0 01 √21 0 1 01 0 (a) What is the rank of A? (b) max||||1||AZ|| (c) det(AA) (d) What are the eigenvalues of A¹ A? V = -1/√3 (e) Find an orthonormal basis for Row(4). 1/√3 1/√2 1/√6] 0 2/√6. 1/√3 -1/√2 1/√6] (f) Find an orthonormal basis for Nul(A¹). Give an example of a symmetric 3 x 3 matrix A such that: • the corresponding quadratic form Q(z) = A is negative semi-definite and has no cross product terms; • the range of the corresponding linear transformation T(7) = Az is 2-dimensional; and • one of the eigenvalues of A has algebraic multiplicity equal to 2. A Find the minimum value of Q(z) = 4, on the unit sphere in R³. Supplementary Problems - Ch. 7 and Google PageRank. Your initials: You do not need to justify your reasoning for questions on this page. 4. Let A = UEV, where Σ= U √60 0 020 000 00 0 [10-1 0 01 √21 0 1 01 0 (a) What is the rank of A? (b) max||||1||AZ|| (c) det(AA) (d) What are the eigenvalues of A¹ A? V = -1/√3 (e) Find an orthonormal basis for Row(4). 1/√3 1/√2 1/√6] 0 2/√6. 1/√3 -1/√2 1/√6] (f) Find an orthonormal basis for Nul(A¹).

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To construct a symmetric 3x3 matrix A that satisfies the given conditions one possible example is A ... View the full answer