explain why each of the following statemens is either true of false.(adsbygoogle = window.adsbygoogle || []).push({});

(a) if A is a 3X3 matrix and {v1, v2, v3} is linearly dependent set of vectors in R^3, then {Av1, Av2, Av3} is also a linearly dependent set.

(b) if A is a 3X3 invertible matrix and {v1, v2, v3} is a linearly independent set of vectors in R^3, then {Av1, Av2, Av3} is also a linearly independent set.

(c) if A is a 3X3 matrix and {v1, v2, v3} is a linearly independent set of vectors in R^3 for which {Av1, Av2, Av3} is also a linearly independent set, then the matrix A must be invertible.

(d) If A is a 3X3 matrix and {v1, v2} is a linearly independent set of vectors in R^3 for which {Av1, Av2} is also a linearly independent set, then the matrix A must be invertible.

(e) if A and B are 3X3 matrices and the product AB is known to be invertible, then it follows that B is also invertible.

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# Explain true of false

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