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Rezz5

how to find the rank of a matrix?

  • one year ago
  • one year ago

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  1. Rezz5
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    \[\left[\begin{matrix}1 & -1 &2\\ 3 & -3&6\\-2&2&4\end{matrix}\right]\]

    • one year ago
  2. shubhamsrg
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    even i want to learn this.. so *bookmark*

    • one year ago
  3. slaaibak
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    Do the gauss jordan elimination method and check how many leading ones there are

    • one year ago
  4. amistre64
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    ""Suppose that A is a matrix then the row space of A and the column space of A will have the same dimension. We call this common dimension the rank of A and denote it by rank (A)." http://tutorial.math.lamar.edu/Classes/LinAlg/FundamentalSubspaces.aspx

    • one year ago
  5. amistre64
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    if the row and col have different dimensions, then rank (A) is equal or smaller than the smaller value

    • one year ago
  6. slaaibak
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    By inspection, it would be 2. Row 2 is a multiple of row one. row 3 is not a multiple or linear combination of row 1 or 2 so therefore, row 1 and 3 are linearly independent. hence, rank = 2

    • one year ago
  7. Servet
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    As people have suggested, get it down to reduced form and see how many leading 1's there is :) that is the rank.

    • one year ago
  8. Rezz5
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    So if i get something like 1 4 6 0 3 4 0 0 0 rank is 2? or 2 5 7 0 0 0 0 0 0 rank is 1? Or 1 4 5 1 0 0 1 0 4 rank is 3?

    • one year ago
  9. slaaibak
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    no. the third one is incorrect

    • one year ago
  10. amistre64
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    given an nxm matrix rankA + nullA = m

    • one year ago
  11. Rezz5
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    third would be 2?

    • one year ago
  12. slaaibak
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    soz third one is correct. it is 3

    • one year ago
  13. slaaibak
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    1 4 5 1 0 0 1 0 4 1 0 0 1 4 5 1 0 4 1 0 0 0 4 5 0 0 4

    • one year ago
  14. Rezz5
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    okay, i think i undertand now so we reduce to row echelon form and do leading 1's then count the smallest number of rows?

    • one year ago
  15. Rezz5
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    so 1 0 0 0 4 5 0 0 4 becomes 1 0 0 0 1 5/4 0 0 1 and that has three 1's so rank is 3

    • one year ago
  16. slaaibak
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    counting leading ones would suffice. yes, above is correct

    • one year ago
  17. Rezz5
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    thanks all!!

    • one year ago
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