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  3. 3. true or false? all vectors below are in rn for

3. True or false? All vectors below are in Rn for some n. If your answer...

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Advance Math

3. True or false? All vectors below are in Rn forsome n. If your answer is “True”, explain why. If your answer is“False”, give a counterexample. Please specify for all if the givenstatement is true or false, thank you!

(1) If two vectors are linearly independent, then they areorthogonal.

(2) If x is orthogonal to both u and v, then x must beorthogonal to u − v.

(3) If W is a subspace of Rn, then W and W^⊥(Wtranspose) have no vectors in common.

(4) If z is orthogonal to v1 and v2 and ifW =span(v1,v2), the z must be in W^⊥​​​​​​​(Wtranspose) .

(5) ∥cv∥ = c∥v∥ for all scalars c and vectors v in Rn.

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