Symmetric and skew-symmetric matricesHard
Cardinality of Matrix Set Unions
Let M denote the set of all real matrices of order 3 × 3 and let S = {–3, –2, –1, 1, 2}. Let
S1 = {A = [aij]∈M : A = AT and aij ∈ S,
i, j}
S2 = {A = [aij]∈M : A = –AT and aij ∈ S,
i, j}
S3 = {A = [aij]∈M : a11 + a22 + a33 = 0 and aij ∈ S,
i,j}
If n(S1 ∪ S2 ∪ S3) = 125α, then α equals.
S1 = {A = [aij]∈M : A = AT and aij ∈ S,
i, j}S2 = {A = [aij]∈M : A = –AT and aij ∈ S,
i, j}S3 = {A = [aij]∈M : a11 + a22 + a33 = 0 and aij ∈ S,
i,j}If n(S1 ∪ S2 ∪ S3) = 125α, then α equals.
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