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For each of the following statements, determine whether the statement is true or false. If you...

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Basic Math

For each of the following statements, determine whether thestatement is true or false. If you say the statement is true,explain why and if you say it is false, give an example toillustrate.

(a) If {u, v} is a linearly independent set in a vector space V,then the set {2u + 3v, u + v} is also a linear set independent ofV.

(b) Let A and B be two square matrices of the same format. Thendet (A + B) = det (A) + det (B).

(c) It is possible to find a non-zero square matrix A such thatA^2 = 0.

(d) Let V be a vector space. If {v1, v2,. . . , vn} (with n ≥ 1)is a base of V and if {w1, w2,. . . , wm} is a generator system ofV then n ≤ m.

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