Let B be a square matrix  (True or False): 1)The eigenvalues of 10B, are 10 times the eigenvalues of B, i.e., λ(10B) = 10λ(B). 2). B and 10B have the same eigenvectors. 3) If B is nonsingular it may have a zero eigenvalue.

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A: Solution given by you has many ambiguity in the definitions. So I rewrote the whole thing. Thanks

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A: Given: The Information that leads to the required proof.We need to prove the equations marked in…

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Q: (b) Find a simplified formula for n. Σ(14) i (c) Use induction to prove your formula from (b).…

A: ∑i=1n1i-1i+1=1-12+12-13+.....+1n-1n+1=1-12+12-13+....-1n+1n-1n+1=1-1n+1=nn+1 Therefore…

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A: (ii) asked and answered.