Linear transformation Test 1 [on hold]

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I am not sure how to solve this question. Can anyone give me some hints or help me to solve it.




Let $S$ be the standard bases $(1,0,0),(0,1,0),(0,0,1)$ for the vector space $mathbb R^3$, and let $f : mathbb R^3tomathbb R^3$ be a linear transformation defined by $$f(x, y, z) = (3x + 2y + 4z, 2x + 2z, 4x + 2y + 3z).$$



  1. Find the matrix $_S[f]_S$.

  2. Show that $8$ is an eigenvalue of $f$ and find the remaining eigenvalues.

  3. Find a basis $T$ for $mathbb R^3$ such that $_T[f]_T$ is diagonal, and calculate $_T[f]_T$.




vector-spaces




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put on hold as off-topic by José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 2




    Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    2 days ago






  • 1




    If you have some notes on the topic, then you should also have some idea on how to approach the problem. Have you tried anything?
    – AnyAD
    2 days ago






  • 1




    Please show what you tried. This question is 100% technical. You don't need to think here, it's simply using the definitions and calculating.
    – Mark
    2 days ago










  • I don't have note with me at the moment so I have no idea where to start.
    – Benny.Y
    yesterday














up vote
-6
down vote

favorite












I am not sure how to solve this question. Can anyone give me some hints or help me to solve it.




Let $S$ be the standard bases $(1,0,0),(0,1,0),(0,0,1)$ for the vector space $mathbb R^3$, and let $f : mathbb R^3tomathbb R^3$ be a linear transformation defined by $$f(x, y, z) = (3x + 2y + 4z, 2x + 2z, 4x + 2y + 3z).$$



  1. Find the matrix $_S[f]_S$.

  2. Show that $8$ is an eigenvalue of $f$ and find the remaining eigenvalues.

  3. Find a basis $T$ for $mathbb R^3$ such that $_T[f]_T$ is diagonal, and calculate $_T[f]_T$.




vector-spaces




share|cite|improve this question













put on hold as off-topic by José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 2




    Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    2 days ago






  • 1




    If you have some notes on the topic, then you should also have some idea on how to approach the problem. Have you tried anything?
    – AnyAD
    2 days ago






  • 1




    Please show what you tried. This question is 100% technical. You don't need to think here, it's simply using the definitions and calculating.
    – Mark
    2 days ago










  • I don't have note with me at the moment so I have no idea where to start.
    – Benny.Y
    yesterday












up vote
-6
down vote

favorite









up vote
-6
down vote

favorite











I am not sure how to solve this question. Can anyone give me some hints or help me to solve it.




Let $S$ be the standard bases $(1,0,0),(0,1,0),(0,0,1)$ for the vector space $mathbb R^3$, and let $f : mathbb R^3tomathbb R^3$ be a linear transformation defined by $$f(x, y, z) = (3x + 2y + 4z, 2x + 2z, 4x + 2y + 3z).$$



  1. Find the matrix $_S[f]_S$.

  2. Show that $8$ is an eigenvalue of $f$ and find the remaining eigenvalues.

  3. Find a basis $T$ for $mathbb R^3$ such that $_T[f]_T$ is diagonal, and calculate $_T[f]_T$.




vector-spaces




share|cite|improve this question













I am not sure how to solve this question. Can anyone give me some hints or help me to solve it.




Let $S$ be the standard bases $(1,0,0),(0,1,0),(0,0,1)$ for the vector space $mathbb R^3$, and let $f : mathbb R^3tomathbb R^3$ be a linear transformation defined by $$f(x, y, z) = (3x + 2y + 4z, 2x + 2z, 4x + 2y + 3z).$$



  1. Find the matrix $_S[f]_S$.

  2. Show that $8$ is an eigenvalue of $f$ and find the remaining eigenvalues.

  3. Find a basis $T$ for $mathbb R^3$ such that $_T[f]_T$ is diagonal, and calculate $_T[f]_T$.





vector-spaces





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago









an4s

2,0281317




2,0281317









asked 2 days ago









Benny.Y

1




1




put on hold as off-topic by José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, amWhy, Jyrki Lahtonen, Mohammad Riazi-Kermani, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 2




    Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    2 days ago






  • 1




    If you have some notes on the topic, then you should also have some idea on how to approach the problem. Have you tried anything?
    – AnyAD
    2 days ago






  • 1




    Please show what you tried. This question is 100% technical. You don't need to think here, it's simply using the definitions and calculating.
    – Mark
    2 days ago










  • I don't have note with me at the moment so I have no idea where to start.
    – Benny.Y
    yesterday












  • 2




    Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
    – José Carlos Santos
    2 days ago






  • 1




    If you have some notes on the topic, then you should also have some idea on how to approach the problem. Have you tried anything?
    – AnyAD
    2 days ago






  • 1




    Please show what you tried. This question is 100% technical. You don't need to think here, it's simply using the definitions and calculating.
    – Mark
    2 days ago










  • I don't have note with me at the moment so I have no idea where to start.
    – Benny.Y
    yesterday







2




2




Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
– José Carlos Santos
2 days ago




Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures.
– José Carlos Santos
2 days ago




1




1




If you have some notes on the topic, then you should also have some idea on how to approach the problem. Have you tried anything?
– AnyAD
2 days ago




If you have some notes on the topic, then you should also have some idea on how to approach the problem. Have you tried anything?
– AnyAD
2 days ago




1




1




Please show what you tried. This question is 100% technical. You don't need to think here, it's simply using the definitions and calculating.
– Mark
2 days ago




Please show what you tried. This question is 100% technical. You don't need to think here, it's simply using the definitions and calculating.
– Mark
2 days ago












I don't have note with me at the moment so I have no idea where to start.
– Benny.Y
yesterday




I don't have note with me at the moment so I have no idea where to start.
– Benny.Y
yesterday















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