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3. True and False. Explanations are requied. (a) For a nondiagonalizable 3 * 3 matrix A, the number of eigenvalues (counted by multiplicity) is still 3. (b) A linear system with (3 variables and 2 equations) is inconsistent if there is only one pivots in its coefficient matrix. (c) Upper trianglar matrices are always diagonalizable. (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and c are parallel. (e) Suppose a, b, c are non-zero vectors in R4, and a is perpendicular to both of b, c. Then band c are parallel.

3. True and False. Explanations are requied. (a) For a nondiagonalizable 3 * 3 matrix A, the number of eigenvalues (counted by multiplicity) is still 3. (b) A linear system with (3 variables and 2 equations) is inconsistent if there is only one pivots in its coefficient matrix. (c) Upper trianglar matrices are always diagonalizable. (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and c are parallel. (e) Suppose a, b, c are non-zero vectors in R4, and a is perpendicular to both of b, c. Then band c are parallel.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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3. True and False. Explanations are requied. • (a) For a nondiagonalizable 3 * 3 matrix A, the number of eigenvalues (counted by multiplicity) is still 3. • (b) A linear system with (3 variables and 2 equations) is inconsistent if there is only one pivots in its coefficient matrix. • (c) Upper trianglar matrices are always diagonalizable. • (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and c are parallel. • (e) Suppose a, b, c are non-zero vectors in R4, and a is perpendicular to both of b, c. Then b and c are parallel.
Transcribed Image Text:3. True and False. Explanations are requied. • (a) For a nondiagonalizable 3 * 3 matrix A, the number of eigenvalues (counted by multiplicity) is still 3. • (b) A linear system with (3 variables and 2 equations) is inconsistent if there is only one pivots in its coefficient matrix. • (c) Upper trianglar matrices are always diagonalizable. • (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and c are parallel. • (e) Suppose a, b, c are non-zero vectors in R4, and a is perpendicular to both of b, c. Then b and c are parallel.
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