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Determine if each of the following statements is true or false. If it’s true, explain why....

Determine if each of the following statements is true or false. If it’s true, explain why. If it’s false explain why not, or simply give an example demonstrating why it’s false

(a) If λ=0 is not an eigenvalue of A, then the columns of A fo ma basis of R^n.

(b) If u, v ∈ R^3 are orthogonal, then the set {u, u − 3v} is orthogonal.

(c) If S1 is an orthogonal set and S2 is an orthogonal set with S1 ∩S2 = φ, then S1 ∪S2 is an orthogonal set.

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