incorrect result in solving system using MATLAB ?

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Eliza 2017-11-14

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评论： Steven Lord 2017-11-16

I am trynig to solve the following system (mat=coefficient matrix,B=output matrix)

mat =
       1     2     6
       2     5    14
       5     7    24
B=
   0
   0
   0

the expected result is not zeros for sure because this system is linear dependent . And I used mat/B and linsolve(mat,B).However , I have got the answer

and this warning

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =
1.009294e-18.

could any one help me why I got this result and what I should to get the correct answer?

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Answer 1

Torsten 2017-11-15

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在 MATLAB Online 中打开

Try

Z = null(mat)

It should give you a vector Z different from the zero vector that solves

mat*Z = 0

Best wishes

Torsten.

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Eliza 2017-11-16

I have got Z=-0.6667 -0.6667 0.3333 . However,I was having some problem in understanding null space. I was expect the result as I did it manually .So thanks all.

Steven Lord 2017-11-16

Was the result of null(mat, 'r') closer to what you found when you did it manually? From the help for the null function:

"The orthonormal basis is preferable numerically, while the rational basis may be preferable pedagogically."

The rational basis is what you get when you add the 'r' flag.

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Answer 2

Steven Lord 2017-11-14

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That answer is one solution to your system of equations. It is not the only solution to that system.

If you add x and any linear combination of columns from the nullspace of your matrix that will be another solution to your system. Take a look at the null function for more information.

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Answer 3

Walter Roberson 2017-11-14

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编辑：Walter Roberson 2017-11-14

rank(mat) is 2 because the third column is twice the sum of the other two columns. You cannot use the \ operator with singular matrix.

If the b matrix was not all zero then pinv(mat)*b might work, but since it is all 0 the result is going to be all 0.

With the all-zero b, you are effectively looking null spaces, for which you should look at null(mat)

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Eliza 2017-11-14

My goal of solving this system is to prove that it is not linear independent ,so I make it equal to b matrix which is equal to zero and if I get result rather than zeros this means it is Linear dependent ,but the result gave me zeros .All what I want now is getting any result except zeros .