Question

Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. Verify that A = [-8 3; -19 8] is similar to itself by finding a T such that A = T^-1 AT. T = [ ; ] We know that A and B = [-2 -3; -1 2] are similar since A = P^-1 BP where P = [1 0; 2 -1]. Verify that B ~ A by finding an S such that B = S^-1 AS. S = [ ; ] We also know that B and C = [2 3; 1 -2] are similar since B = Q^-1 CQ where Q = [2 1; -3 -2]. Verify that A ~ C by finding an R such that A = R^-1 CR. R = [ ; ]

          Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. Verify that A = [-8 3; -19 8] is similar to itself by finding a T such that A = T^-1 AT. T = [ ; ] We know that A and B = [-2 -3; -1 2] are similar since A = P^-1 BP where P = [1 0; 2 -1]. Verify that B ~ A by finding an S such that B = S^-1 AS. S = [ ; ] We also know that B and C = [2 3; 1 -2] are similar since B = Q^-1 CQ where Q = [2 1; -3 -2]. Verify that A ~ C by finding an R such that A = R^-1 CR. R = [ ; ]

Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. Verify that A = [-8 3; -19 8] is similar to itself by finding a T such that A = T^-1 AT. T = [ ; ] We know that A and B = [-2 -3; -1 2] are similar since A = P^-1 BP where P = [1 0; 2 -1]. Verify that B A by finding an S such that B = S^-1 AS. S = [ ; ] We also know that B and C = [2 3; 1 -2] are similar since B = Q^-1 CQ where Q = [2 1; -3 -2]. Verify that A C by finding an R such that A = R^-1 CR. R = [ ; ]

Added by Roy K.

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