Which of the following subsets of the vector space V=R^2×2 over the field R is not a vector subspace? (a) The set of all upper triangular matrices from V. (b) The set of all diagonal matrices from V. (c) The set of all matrices from V with zero determinant. (d) The set of all matrices from V with zero trace. (e) The set of all matrices from V having coefficient 0 at the intersection of the first row and the first column.

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Chapter2: Second-order Linear Odes
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Which of the following subsets of the vector space V=R^2×2 over the field R is not a vector subspace?

(a) The set of all upper triangular matrices from V.

(b) The set of all diagonal matrices from V.

(c) The set of all matrices from V with zero determinant.

(d) The set of all matrices from V with zero trace.

(e) The set of all matrices from V having coefficient 0 at the intersection of the first row and the first column.

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