Let A be an 3 by 3 matrix. Select all true statements below.A. If A is diagonalizable, then A has 3 distinct real eigenvalues.B. If A has 3 linearly independent eigenvectors, then A is diagonalizable.C. The matrix A may or may not be diagonalizable.D. The matrix A is certainly diagonalizable.E. If A has 3 distinct real eigenvalues, then A is diagonalizable.OF. If A is diagonalizable, then A has 3 linearly independent eigenvectors.G. None of the above

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Answered: Let A be an 3 by 3 matrix. Select all…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For this exercise assume that the matrices are all nxn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer. If the equation Ax = b has at least one solution for each b in R, then the solution is unique for each b. Choose the correct answer below. A. The statement is true. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then matrix A is invertible. If A is invertible, then according to the invertible matrix theorem the solution is unique for each b. OB. The statement is true, but only for x 0. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R, then the equation Ax = 0 does not only have the trivial solution. OC. The statement is false. By the…
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Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. The statement is false. The multiplicity of a root r of the characteristic equation of A is the number of eigenvectors corresponding to that root. The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A. OThe statement is false. The multiplicity of a rootr of the characteristic equation. of A is called the geometric multiplicity of r as an eigenvalue of A.

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