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General solution ~ ~ ~ Linear algebra in advanced mathematics
(-4,9/4,3,0) in the figure is wrong. It seems that x3=3 and x4=0, but you should get X 1 =- 12. In this way, it is understood that (-12, 9/4, 3,0) = 3/4 (-16,3,4,0).

It should be noted here that when the homogeneous linear equation system Ax=0 has a non-zero solution, the expression of its general solution is not unique, as long as the following conditions are met:

1, and the structure of the general solution is x = k1ξ1+K29582+...+Kr ξ r.

2.ξ 1,ξ2, ..., ξr are all nonzero solutions of Ax=0, and they are linearly independent.

3.r=n-r(A), where n is the number of unknowns and r(A) is the rank of coefficient matrix a.

In addition, in ξ 1, ξ2, ..., ξr, fractions and common factors greater than 1 generally do not appear, because these denominators and multiples can be divided by the previous coefficients K 1, K2, ..., Kr.