the transpose of a matrix A = [ai,j] is defined by AT = [aj,i]. For instance...

   

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the transpose of a matrix A = [ai,j] is defined by AT = [aj,i]. For instance [ c a b C d = [ i a C b d . A matrix M is called symmetric if M = 1. Show that V = {2 x 2 symmetric matrices } together with usual addition and scaler multiplication of matrices is a vector space. 2. Find a basis of V. Exercise 2 Find the coordinates of v = (1,2,3) in the basis B = {(1,0,1), (0, -1, 0), (1, 0, 1)}, the transpose of a matrix A = [ai,j] is defined by AT = [aj,i]. For instance [ c a b C d = [ i a C b d . A matrix M is called symmetric if M = 1. Show that V = {2 x 2 symmetric matrices } together with usual addition and scaler multiplication of matrices is a vector space. 2. Find a basis of V. Exercise 2 Find the coordinates of v = (1,2,3) in the basis B = {(1,0,1), (0, -1, 0), (1, 0, 1)},