i would solve a linear equation system like this:
x_1*3+x_2*4+x_3*5+x_4*6+x_6*2=0
x_1*21+x_2*23+x_3*45+x_4*37*+x_6*0=0
x_1*340+x_2*24+x_3*25+x_4*31+x_6*0=0
x_1*32+x_2*45+x_3*5+x_4*6+x_7*2=0
x_1*9+x_2*11+x_3*13+x_4*49+x_7*0=0
x_1*5+x_2*88+x_3*100+x_4*102+X_7*2=0
[x_1][x_2][x_3] [x_4] [,5]
[1,] 3 4 5 6 2
[2,] 21 23 45 37 0
[3,] 340 24 25 31 0
[4,] 32 45 5 6 2
[5,] 9 11 13 49 0
[6,] 5 88 100 102 2
i use solve this linear homogeneous equation system with MASS::null(t(M)
,
but the problem is that find x_1....x_4, but x_5 find only one solution but i need different three value that is x_5,1,x_5,2 and x_5,3.
value of matrix are random, and they can be changed
With the update which shows you've got 5 equations with 7 unknowns, it's obvious that there is a multidimensional surface of solutions.
I fear I don't have code to calculate that surface, but let me toot my own horn and offer the
ktsolve
package. For any given set of inputs from your { $x_1, x_2, ...x_7$ } [ah rats no latex markdown] , enter a collection of known values andktsolve
will run a back-solver (usuallyBB
) to find the unknowns.So if you can feed your problem a selected set of any two of {X_5, X_6, X_7}, you can find all five of the other values.