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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. AT is not invertible.) PR = 0, then P,Q, and R all lie 4.3 True or False: If P, Q, and R are distinct points in R³ so that PQ > 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. AT is not invertible.) PR = 0, then P,Q, and R all lie 4.3 True or False: If P, Q, and R are distinct points in R³ so that PQ > on a single line.

Advanced Engineering Mathematics
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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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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