n 1. Consider the 3x3 matrix la) For each 3x3 matrix. la 11 A = a a

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1. Consider the 3x3 matrix la) For each 3x3 matrix. la 11 A = a a 12 13 C₂5 ani agz 21 asi ase ass/s s. (:) = calculate SA and AS. (b) In the vector space M₂ (R) of real 3x3 matrices, Ishow that the subset. W = {A&M (TR) | SA=AS} 3x3 forms a vector subspace, and find a basis for W.. (C) Define a function f: M₂ (TR) → M₂ (TR) by setting f(A) = SA-AS, for all A in the vector space M₂ (TR). Show that this function is linear, and determine its rank. 1. Consider the 3x3 matrix la) For each 3x3 matrix. la 11 A = a a 12 13 C₂5 ani agz 21 asi ase ass/s s. (:) = calculate SA and AS. (b) In the vector space M₂ (R) of real 3x3 matrices, Ishow that the subset. W = {A&M (TR) | SA=AS} 3x3 forms a vector subspace, and find a basis for W.. (C) Define a function f: M₂ (TR) → M₂ (TR) by setting f(A) = SA-AS, for all A in the vector space M₂ (TR). Show that this function is linear, and determine its rank.

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