Which of the following sets of 2x2 matrices are vector spaces? Justify your answer. i) W = {[a b; c d] | a + b = 3c - d} ii) All 2x2 matrices A such that Ax = 0 has a nontrivial solution. iii) All 2x2 diagonal matrices.
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To be a vector space, the set must be closed under addition and scalar multiplication, and it must contain the zero vector. Show more…
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