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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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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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