3 Define the set S of matrices by S = {A = (aij) = M₂ (R): a11 = a22, a12 = -a21}. It turns out that S is a ring, with the operations of matrix addition and multiplication. (a) Write down two examples of elements of S, and compute their sum and product (b) Prove the additive and multiplicative closure laws for S.

Q: b) Let A, B, C, DE RX" be invertible matrices and suppose A" = c" (A-' D)")" B. %3D Solve for D in…

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Q: Let M₂ (R) be the set of all 2 x 2 matrices over R. Let + denote the usual addition of matrices and…

A: Explained below

Q: Prove that for a diagonal matrix, the 1-,2-,∞- and -norms are the same.

A: We are given a diagonal matrix D. We wish to show that D1=D2=D∞ If we write D=d10⋯00d2⋱⋮⋮⋱⋱00⋯dn…

Q: Let A and B be matrices with size 3 x 3. If only one of these matrices are diagonalizable and if…

A: Given, A and B be matrices with size 3×3det(A-λI3)=(λ-2)(λ2-9)det(B-λI3)=(λ-3)2(λ+2)(a) Eigenvalues…

Q: 3. Use summation notation to prove that the product of two upper-triangular matrices is…

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Q: Which of the following matrices have characterestic polynomial p(A) =A-10A+ 1 Select one: O a. T0 1…

A: To find the correct option

Q: 1. Are the following matrices diagonalisable? Explain your answer. 2 0 50 1] a) A =-2 3 -1 -2 0 3 c)…

A: A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is…

Q: 7. Let A = (; ) (a) Express A- as a product of elementary matrices. (b) Express A as a product of…

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Q: Let T: R² R² be defined by T 3 -{[]).H]} and C Given Pc [T](PB (u)) = ([^]) Ex: 5 -x₁ + 2x₂ [-3x1 +…

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