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) Let A be a n xn matrix. If (51 – A) is not invertible, then CA(5) = 0. (b) Let A, P, D be n xn matrices. If PAP = D, then det A = det D. (c) Let A be a 5x5 matrix. If A has only one distinct eigenvalues, then A is not diagonalizable.

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Q: A and B are n x n invertible matrices, then the equality (A +B) (A – B) = A? – B? always true.

A: No this false ,

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A: 1a+1a-24

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A: Given C = A - 2B

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Q: q4: If  det(A) =|A|= 0, then A is called a non-singular matrix  True  False

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.