a) Let Tbe a linear mapping of Vninto Vm.Prove: If v1, ..., vk are linearly dependent vectors of Vn, then T(v1),..., T(vk) are linearly dependent vectors of Vm.
Is the converse true? Explain.
b) Let A be a nonsingular n x n matrix. Show that if v1, …, vk are vectors of Vn, then they are linearly independent if and only if Av1, ..., Avk are linearly independent.
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