Find a solution to the following system or prove that none exists: x 1 − x 2 ≤ 4 x 1 − x 5 ≤ 2 x 2 − x 4 ≤ − 6 x 3 − x 2 ≤ 1 x 4 − x 1 ≤ 3 x 4 − x 3 ≤ 5 x 4 − x 5 ≤ 10 x 4 − x 3 ≤ − 4 x 5 − x 4 ≤ − 8

Question

Find a solution to the following system or prove that none exists:                              x          1                −                  x          2                                    ≤        4                                      x          1                −                  x          5                                    ≤        2                                      x          2                −                  x          4                                    ≤        −        6                                      x          3                −                  x          2                                    ≤        1                                      x          4                −                  x          1                                    ≤        3                                      x          4                −                  x          3                                    ≤        5                                      x          4                −                  x          5                                    ≤        10                                      x          4                −                  x          3                                    ≤        −        4                                      x          5                −                  x          4                                    ≤        −        8

Strehaiau10p7 · Accepted Answer

Suppose a solution exists. Then add up the third, fourth, and eighth constraints  (      x    2    −      x    4    )  +  (      x    3    −      x    2    )  +  (      x    4    −      x    3    )  ≤  −  6  +  1  −  4  to obtain the contradiction   0  ≤  −  9.

homosepian9wlgl · Accepted Answer

You can add       x    i    −      x    j    ≤  a  and       x    j    −      x    k    ≤  b to get       x    i    −      x    k    ≤  a  +  b and if you have       x    i    −      x    k   anywhere.So       x    1    −      x    2    +      x    2    −      x    4    =      x    1    −      x    4    ≤  4  +  (  −  6  )  =  −  2. And       x    4    −      x    1    ≤  3 so   −  3  ≤      x    1    −      x    4    ≤  −  2.And       x    1    −      x    5    +      x    5    −      x    4    =      x    1    −      x    4    ≤  2  +  (  −  8  )  =  −  6. Which contradicts the above.

Find a solution to the following system or prove that none exists: <mtable columnalign="right le

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Answer & Explanation

New Questions in Algebra I