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For each given vector space, identify the positive integer k such that the vector space is roughly "the same as" or "corresponds to" the vector space Rk. (Later we will make this correspondence more precise and call it "isomorphism.") The set M2 times 3 of 2 times 3 matrices with real entries, under the usual matrix addition and scalar multiplication. The M m times n of m times n matrices with real entries. The set C = {(x y 0 z)|x, y, z ER}. B = {(x y 0 z)|x, y, z ER and x + y + z = 0}.

Show transcribed image text For each given vector space, identify the positive integer k such that the vector space is roughly "the same as" or "corresponds to" the vector space Rk. (Later we will make this correspondence more precise and call it "isomorphism.") The set M2 times 3 of 2 times 3 matrices with real entries, under the usual matrix addition and scalar multiplication. The M m times n of m times n matrices with real entries. The set C = {(x y 0 z)|x, y, z ER}. B = {(x y 0 z)|x, y, z ER and x + y + z = 0}.