1 / 12

Determine the nullspace of B where B

~. Determine the nullspace of B where B. x 1 x 2 x 3 x 4 x 5. 0 0 0. ~. Solve: B x = 0 where B. x 1 x 2 x 3 x 4 x 5. x 1 x 1 x 1 0 1 0 x 2 -8 x 4 0 - 8 x 4 0 -8

amory
Download Presentation

Determine the nullspace of B where B

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ~ Determine the nullspace of B where B x1x2x3 x4 x5

  2. 0 0 0 ~ Solve: B x = 0 where B x1x2x3 x4 x5 x1x1x101 0 x2 -8x40-8x40 -8 x3-6x40 -6x40 -6 x4x4 0 x4 0 1 x500 0 0 0 = = + = + x1 x4

  3. 0 0 0 ~ Solve: B x = 0 where B x1x2x3 x4 x5 x1 1 0 x20 -8 x30 -6 x40 1 x50 0 = + x1 x4

  4. 0 0 0 ~ Solve: B x = 0 where B x1x2x3 x4 x5 { |} x1 1 0 x20 -8 x30 -6 x40 1 x50 0 = + Nul B x1 x4 x1, x4 in R

  5. 0 0 0 ~ Solve: B x = 0 where B x1x2x3 x4 x5 { |} 1 0 0 -8 0 -6 0 1 0 0 = + Nul B x1 x4 x1, x4 in R

  6. 0 0 0 ~ Solve: B x = 0 where B x1x2x3 x4 x5 { } 1 0 0 -8 0 -6 0 1 0 0 = span , Nul B

  7. ~ Solve: E x = 0 where E x1x2x3x4x5x6x7 x1x1 10 0 x25x4- 5x70 5 -5 x3-7x4 + 3x70 -7 3x4x4 0 1 0 x500 0 0 x6 x70 0 1 x7 x70 0 1 x1 x4 x7 = = + +

  8. NulE =

  9. Determine the column space of E where E IF POSSIBLE ~ x1x2x3x4x5x6x7 Note: We don’t know the original matrix E. We only know REF of E.

  10. Determine the column space of B where B IF POSSIBLE ~ x1x2x3 x4 x5 Note: We don’t know the original matrix B. We only know REF of B. But

  11. = Determine the column space of A Column space of A = col A = col A = span , , , = c1+ c2+c3 + c4 ciin R { } { }

  12. = Determine the column space of A Put A into echelon form: A basis for col A consists of the 3 pivot columns from the original matrix A. Thus basis for col A = R2 – R1 R2 R3 + 2R1  R3 { }

More Related