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

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

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

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

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

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

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

Expert Solution

Colby Messinger answered 1 year ago

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