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Determine if the statements below are true or false. Make sure to justify your answers! You will receive no credit for simply selecting "true" or "false", or providing little explanation. 4.1 True or False: If A is a 4 x 4 matrix with only one eigenvalue, then A is not diagonalizable. 4.2 True or False: If T : R³ → R3 is a linear transformation so that T(e) = T(e2- e3), then T is not invertible (i.e. A is not invertible.) 4.3 True or False: If P, Q, and R are distinct points in R so that PQ > PR = 0, then P,Q, and R all lie on a single line.

Determine if the statements below are true or false. Make sure to justify your answers! You will receive no credit for simply selecting "true" or "false", or providing little explanation. 4.1 True or False: If A is a 4 x 4 matrix with only one eigenvalue, then A is not diagonalizable. 4.2 True or False: If T : R³ → R3 is a linear transformation so that T(e) = T(e2- e3), then T is not invertible (i.e. A is not invertible.) 4.3 True or False: If P, Q, and R are distinct points in R so that PQ > PR = 0, then P,Q, and R all lie on a single line.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.5: Applications
Problem 74EQ
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4 Determine if the statements below are true or false. Make sure to justify your answers! You will receive no credit for simply selecting "true" or "false", or providing little explanation. 4.1 True or False: If A is a 4 x 4 matrix with only one eigenvalue, then A is not diagonalizable. 4.2 True or False: If T : R3 → R³ is a linear transformation so that T(e1) = T(e2 - e3), then T is not invertible (i.e. AT is not invertible.) 4.3 True or False: If P, Q, and R are distinct points in R so that PQ x PR = 0, then P, Q, and R all lie on a single line.
Transcribed Image Text:4 Determine if the statements below are true or false. Make sure to justify your answers! You will receive no credit for simply selecting "true" or "false", or providing little explanation. 4.1 True or False: If A is a 4 x 4 matrix with only one eigenvalue, then A is not diagonalizable. 4.2 True or False: If T : R3 → R³ is a linear transformation so that T(e1) = T(e2 - e3), then T is not invertible (i.e. AT is not invertible.) 4.3 True or False: If P, Q, and R are distinct points in R so that PQ x PR = 0, then P, Q, and R all lie on a single line.
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