Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Find PA, MA for A = What about over Q? Justify your answers. Select one: 0 1 2 1 20 201 O over R. Is A diagonalisable? Over R we obtain P(x) = (x - √2)(x² + x - 3) which factors further to give 3 distinct real roots. Hence mA = PA and A is diagonalisable. Over Q there are no roots at all so mA = PA but A is not diagonalisable. O Over R we obtain P(x) = (x + 2)(x − √√3)² but (A +213) (A - √313) = 0 so m₁ = (x + 2)(x - √√3) and A is diagonalisable. But over Q we have PA(x) = (x − 3)(x² - 2x + 3) which does not factorise further and A 213 so mA = PA is not the product of distinct linear factors, so not diagonalisable. O Over R we obtain p₁(x) = (x − 3)(x − √3)(x + √3) which has 3 distinct roots. So mA = PA and A is diagonalisable. But over Q we just have PA(x) = (x − 3)(x² - 3) which does not factorise further and A 313 so mA = PA is not the product of distinct linear factors, so A is not diagonalisable. Over R we obtain P₁(x) = (x − 2)(x² + x + 3) which does not factor further, and A ‡ 213 so mд = PÅ is not the product of distinct linear factors, so A is not diagonalisable. The same holds over Q. None of the others apply

Find PA, MA for A = What about over Q? Justify your answers. Select one: 0 1 2 1 20 201 O over R. Is A diagonalisable? Over R we obtain P(x) = (x - √2)(x² + x - 3) which factors further to give 3 distinct real roots. Hence mA = PA and A is diagonalisable. Over Q there are no roots at all so mA = PA but A is not diagonalisable. O Over R we obtain P(x) = (x + 2)(x − √√3)² but (A +213) (A - √313) = 0 so m₁ = (x + 2)(x - √√3) and A is diagonalisable. But over Q we have PA(x) = (x − 3)(x² - 2x + 3) which does not factorise further and A 213 so mA = PA is not the product of distinct linear factors, so not diagonalisable. O Over R we obtain p₁(x) = (x − 3)(x − √3)(x + √3) which has 3 distinct roots. So mA = PA and A is diagonalisable. But over Q we just have PA(x) = (x − 3)(x² - 3) which does not factorise further and A 313 so mA = PA is not the product of distinct linear factors, so A is not diagonalisable. Over R we obtain P₁(x) = (x − 2)(x² + x + 3) which does not factor further, and A ‡ 213 so mд = PÅ is not the product of distinct linear factors, so A is not diagonalisable. The same holds over Q. None of the others apply

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter55: Introduction To Circles
Section: Chapter Questions
Problem 20A: Solve the following exercises based on Principles 11-14, although an exercise may require the...
See similar textbooks
icon
Related questions
Question
Find p₁, mд for A = What about over Q? Justify your answers. Select one: 0 1 2 1 2 0 20 1 O over R. Is A diagonalisable? Over R we obtain P(x) = (x − √2)(x² + x - 3) which factors further to give 3 distinct real roots. Hence mA = PA and A is diagonalisable. Over Q there are no roots at all so mд = PÅ but A is not diagonalisable. O Over R we obtain P(x) = (x + 2)(x − √3)² but (A +213)(A - √313) = 0 so m₁ = (x + 2)(x − √√3) and A is diagonalisable. But over Q we have PA(x) = (x − 3)(x² - 2x + 3) which does not factorise further and A 213 so m₁ = PA is not the product of distinct linear factors, so not diagonalisable. O Over R we obtain p(x) = (x − 3)(x − √√3)(x + √√3) which has 3 distinct roots. So mд = PA and A is diagonalisable. But over Q we just have PA(x) = (x − 3)(x² - 3) which does not factorise further and A 313 so m₁ = PA is not the product of distinct linear factors, so A is not diagonalisable. Over R we obtain P₁(x) = (x − 2)(x²+x+3) which does not factor further, and A 213 so mA = PA is not the product of distinct linear factors, so A is not diagonalisable. The same holds over Q. O None of the others apply
Transcribed Image Text:Find p₁, mд for A = What about over Q? Justify your answers. Select one: 0 1 2 1 2 0 20 1 O over R. Is A diagonalisable? Over R we obtain P(x) = (x − √2)(x² + x - 3) which factors further to give 3 distinct real roots. Hence mA = PA and A is diagonalisable. Over Q there are no roots at all so mд = PÅ but A is not diagonalisable. O Over R we obtain P(x) = (x + 2)(x − √3)² but (A +213)(A - √313) = 0 so m₁ = (x + 2)(x − √√3) and A is diagonalisable. But over Q we have PA(x) = (x − 3)(x² - 2x + 3) which does not factorise further and A 213 so m₁ = PA is not the product of distinct linear factors, so not diagonalisable. O Over R we obtain p(x) = (x − 3)(x − √√3)(x + √√3) which has 3 distinct roots. So mд = PA and A is diagonalisable. But over Q we just have PA(x) = (x − 3)(x² - 3) which does not factorise further and A 313 so m₁ = PA is not the product of distinct linear factors, so A is not diagonalisable. Over R we obtain P₁(x) = (x − 2)(x²+x+3) which does not factor further, and A 213 so mA = PA is not the product of distinct linear factors, so A is not diagonalisable. The same holds over Q. O None of the others apply
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS