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Holtlinalg1 61043 determine if the statement is true

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10.–/1 pointsHoltLinAlg1 6.1.043.Determine if the statement is true or false, and justify your answer.If 0 is an eigenvalue ofA, thenFalse. Consider.0110False. Consider.1001False. Since 0 is an eigenvalue, there exists a nonzero vectorxsuch thatAx= 0, and thusnullity(A) = 0.Ax= 0,nullity(A) > 0.
11.–/1 pointsHoltLinAlg1 6.1.044.Determine if the statement is true or false, and justify your answer.Row operations do not change the eigenvalues of a matrix.True. Since row operations do not change the determinant, the eigenvalues are unchanged.True. Since row operations do not change the row space, the eigenvalues are unchanged.False. Consider, which has eigenvalues 0 and 1, and, which has eigenvalues 0 and 2.0100020010000100.0 01 0
12.–/1 pointsHoltLinAlg1 6.1.045.Determine if the statement is true or false, and justify your answer.If 0 is the only eigenvalue ofA, thenAmust be the zero matrix.
Solution or ExplanationFalse,has only the eigenvalue 0.False. Consider.0010False. Consider.00010 01 0
13.–/1 pointsHoltLinAlg1 6.1.046.Determine if the statement is true or false, and justify your answer.The product of the eigenvalues (counting multiplicities) ofAis equal to the constant term of thecharacteristic polynomial ofA.

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Term
Spring
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Tags
Math, Linear Algebra, Algebra, Characteristic polynomial, Eigenvalue eigenvector and eigenspace

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