I have a Matrix , and I want to multiply this Matrix with something so I can get zeros

% for an example *(pinv(P1))*P1=unity Matrix

I want the same thing : ?*P1=zeros

%This ? should be related to P1 like the above example when we took the peasudo inverse to get the unity matrix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%This is the problem
clc;
clear;
H=[1 2 1;2 3 1;4 2 3;3 2 1];
P1=[3 2 4;2 1 1;5 2 3;2 3 7]
P2=[2 6 1;1 3 5;4 2 1;5 2 1];
HT=H+P1+P2

from this equation I want to get

HT=H+P2

I want to null P1

[Image Analyst]

Original question attached (for after he delete it)

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Walter Roberson]

null(P1)

Note: this may have different number of columns depending on the values in P1. Each column of the result will be independent

[Matthew Worker]

yes I want to null P1 and the function that you wrote is correct but Mathematically what you did to P1 to null it,

the steps of this function (null)

[Matthew Worker]

clc;
clear;
H=[1 2 1;2 3 1;4 2 3;3 2 1];
P1=[3 2 4;2 1 1;5 2 3;2 3 7]
P2=[2 6 1;1 3 5;4 2 1;5 2 1];
HT=H+P1+P2

from this equation I want to get

HT=H+P2

I want to null P1

[Walter Roberson]

format long g
H=[1 2 1;2 3 1;4 2 3;3 2 1];
P1=[3 2 4;2 1 1;5 2 3;2 3 7]

P1 = 4×3

3 2 4 2 1 1 5 2 3 2 3 7

P2=[2 6 1;1 3 5;4 2 1;5 2 1];
nP1 = null(P1.').'

nP1 = 1×4

-0.843274042711568 -0.105409255338946 0.421637021355784 0.316227766016838

nP1 * P1

ans = 1×3

-4.44089209850063e-16 0 4.44089209850063e-16

HT = H + nP1 * P1 + P2

HT = 4×3

3 8 2 3 6 6 8 4 4 8 4 2

HT2 = H + P2

HT2 = 4×3

3 8 2 3 6 6 8 4 4 8 4 2

HT - HT2

ans = 4×3

-4.44089209850063e-16 0 4.44089209850063e-16 -4.44089209850063e-16 0 0 0 0 0 0 0 4.44089209850063e-16

Answer 2

[John D'Errico]

Please stop posting answers when you are making only comments.

In what you claim to have tried:

A=[-3 6 -1 1 7;1 -2 2 3 -1;2 -4 5 8 -4]

A = 3×5

-3 6 -1 1 7 1 -2 2 3 -1 2 -4 5 8 -4

the matrix A has rank 3.

rank(A)

ans = 3

So there is NO matrix you can multiply A with on the left except for the all zero matrix, and get a result of all zeros. That is, there does not exist a non-zero matrix X, such that the product X*A will be entirely zero. This is provable using basic linear algebra.

We can find a non-zero matrix Y such that A*Y will be all zeros. But that was not the question you seem to have posed. Thus...

Y = null(A);
norm(A*Y)

ans = 3.2420e-15

So effectively zero to with floating point precision. If you want an exact solution, since A is composed of integers, we can find one easily enough. Thus...

Ysym = null(sym(A))

Ysym = 

A*Ysym

ans = 

[Matthew Worker]

Walter Roberson first answer, when he find nP1 and multiply it with P1 he got zeros(not exactly but he got zeros) and now, when I found the nul_A it is the same as nP1 but without using the Matlab funcion null, I only used the results in the example form the link above (Where he used RREF) to get the nul_A, and I multiply it with A, but the values was very strange 25,-11,5 and so on

[Walter Roberson]

Be careful about which side your are multiplying on.

MATLAB's null(A) is:

The null space of a matrix contains vectors x that satisfy Ax=0.

Notice that is a right multiplication.

You asked for ?*P1=zeros which is a left multiplication.

[Souarv De]

@John D'Errico Here the answer would come with class sym. How to convert it back in to double?

[Walter Roberson]

A = [-3 6 -1 1 7;1 -2 2 3 -1;2 -4 5 8 -4]

A = 3×5

-3 6 -1 1 7 1 -2 2 3 -1 2 -4 5 8 -4

Ysym = null(sym(A))

Ysym = 

A*Ysym

ans = 

double(ans)

ans = 3×2

0 0 0 0 0 0