Consider the stacked vectors Z = X1 H ,Zn Xn -B Yn = i. Suppose x,...,xn...

 

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Consider the stacked vectors Z₁ = X1 H ,Zn Xn -B Yn = i. Suppose x₁,...,xn are linearly independent (no assumption is made on y₁,..., yn). Can we conclude that the vectors z₁,..., Z, are linearly independent? If yes, pro- vide a proof. If no, give a counterexample. ii. Suppose x₁,..., X are linearly dependent (no assumption is made on y₁,..., yn). Can we conclude that the vectors z₁,..., Zn are linearly dependent? If yes, prove the result. If no, give a counterexample. Consider the stacked vectors Z₁ = X1 H ,Zn Xn -B Yn = i. Suppose x₁,...,xn are linearly independent (no assumption is made on y₁,..., yn). Can we conclude that the vectors z₁,..., Z, are linearly independent? If yes, pro- vide a proof. If no, give a counterexample. ii. Suppose x₁,..., X are linearly dependent (no assumption is made on y₁,..., yn). Can we conclude that the vectors z₁,..., Zn are linearly dependent? If yes, prove the result. If no, give a counterexample.