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

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

(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 of V.

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

(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 of V then n ≤ m.

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Expert Solution

milcah answered 1 year ago

Expert Solution

milcah answered 1 year ago

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