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anonymous

  • 5 years ago

let A = [ 1 2 3 4: 5 6 7 8: -1 -2 -3 -4: -5 -6 -7 -8] as a 4x4 matrix find a basis for the vectorspace NullA

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  1. anonymous
    • 5 years ago
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    u mean null space?

  2. anonymous
    • 5 years ago
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    correct

  3. anonymous
    • 5 years ago
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    i used question 8 on this link: http://abacus.bates.edu/~etowne/031811jayawant205examsoln.pdf as a point of reference, but I'm unsure how to handle two free variables

  4. anonymous
    • 5 years ago
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    we reduce the matrix to reduced echelon form

  5. anonymous
    • 5 years ago
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    [(1 0 -1 -2 \ 0 1 2 3 \ 0 0 0 -0\0 0 0 0)\] which shows two free variables, and that x(1) = x(3) +2x(4) and x(2) = -2x(3)-3x(4)

  6. anonymous
    • 5 years ago
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    there r two non-zero rows, mean that rank=2 since we have rank + nullity =4(order of the matrix) nullity=2

  7. anonymous
    • 5 years ago
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    then does the question even make sense to find the basis for that vectorspace?

  8. anonymous
    • 5 years ago
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    u mean the given matrix?

  9. anonymous
    • 5 years ago
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    for the null

  10. anonymous
    • 5 years ago
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    the link i posted shows how they solved for a 3x3 with one free variable, but im unsure how to proceed with two

  11. anonymous
    • 5 years ago
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    oh i didnt check it:)

  12. anonymous
    • 5 years ago
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    opabrawl u there?

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