Consider the following system of linear equations: x 1 + 2 x 2 + x 3 − 2 x 4 = 10 − x 1 + 2 x 2 + x 3 − x 4 = 6 + x 2 + x 3 = 2Find all its canonical forms and basic solutions.

Question

Consider the following system of linear equations:      x    1    +  2      x    2    +      x    3    −  2      x    4    =  10  −      x    1    +  2      x    2    +      x    3    −      x    4    =  6  +      x    2    +      x    3    =  2Find all its canonical forms and basic solutions.

petyelebxu · Accepted Answer

Use Gaussian Elimination to convert the augmented matrix for this problem into      (                            1                          2                          1                          −          2                          10                                      0                          1                          1                          0                          2                                      0                          0                          1                                                                                                                      1                                                                        ╱                                                                                                            4                                                                                            −          2                      )  The leading 1&#039;s in each row identify the leading variables for each column. The       x    4   variable has no leading 1 in its column and it is called a free variable. Let       x    4    =  t and now find       x    1    ,      x    2   and       x    3   in terms of t.

Consider the following system of linear equations: x_1+2x_2+x_3−2x_4=10, x_1+2x_2+x_3−x_4=6, +x_2+x_3=2 Find all its canonical forms and basic solutions.

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