1. For each of the following statements indicate if it is true or false. If the...

1. For each of the following statements indicate if it is true or false. If the answer is
false, briefly explain why.

(a) (2 points) Let V be a vector space and consider the subspace W = Span{v1, v2, v3, v4}.
If v1 = 2v2 + v3, then {v2, v3, v4} is a basis for W.

(b) (2 points) If A and B are invertible n × n matrices, then A is row equivalent to B.

(c) (2 points) Let P3 be the vector space of all polynomials of degree less than or equal
to 3. If {p1, p2, p3} are linearly independent in P3, then they are a basis of P3.

(d) (2 points) If A is an invertible n × n matrix, then det(A3) > 0.

Expert Solution

Colby Messinger answered 1 year ago

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