references about infinitely many solutions of non-homogeneous linear systems

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I have following system:
$Ax=B$
here A is 4x4 type matrix. If $detA =0$, can i say that "
this system has infinitely many solutions provided $Delta_n=0$ (from adding picture.)"



(Note: I found following picture from internet and i could not see this information about $Delta_x,Delta_y,...$ in any books of linear algebra. So I can not trust whether this information is correct. Can anybody give me references for this additional information about infinitely many solutions )



enter image description here




linear-algebra matrix-equations




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  • It is not true. For example, If $A=0$ and $B$ is a non-zero vector, then $det(A)=0$ and so are all the determinants $Delta_1,...Delta_4$. But the system $Ax=B$ has no solutions.
    – user578878
    Jul 25 at 12:30














up vote
0
down vote

favorite












I have following system:
$Ax=B$
here A is 4x4 type matrix. If $detA =0$, can i say that "
this system has infinitely many solutions provided $Delta_n=0$ (from adding picture.)"



(Note: I found following picture from internet and i could not see this information about $Delta_x,Delta_y,...$ in any books of linear algebra. So I can not trust whether this information is correct. Can anybody give me references for this additional information about infinitely many solutions )



enter image description here




linear-algebra matrix-equations




share|cite|improve this question



















  • It is not true. For example, If $A=0$ and $B$ is a non-zero vector, then $det(A)=0$ and so are all the determinants $Delta_1,...Delta_4$. But the system $Ax=B$ has no solutions.
    – user578878
    Jul 25 at 12:30












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have following system:
$Ax=B$
here A is 4x4 type matrix. If $detA =0$, can i say that "
this system has infinitely many solutions provided $Delta_n=0$ (from adding picture.)"



(Note: I found following picture from internet and i could not see this information about $Delta_x,Delta_y,...$ in any books of linear algebra. So I can not trust whether this information is correct. Can anybody give me references for this additional information about infinitely many solutions )



enter image description here




linear-algebra matrix-equations




share|cite|improve this question











I have following system:
$Ax=B$
here A is 4x4 type matrix. If $detA =0$, can i say that "
this system has infinitely many solutions provided $Delta_n=0$ (from adding picture.)"



(Note: I found following picture from internet and i could not see this information about $Delta_x,Delta_y,...$ in any books of linear algebra. So I can not trust whether this information is correct. Can anybody give me references for this additional information about infinitely many solutions )



enter image description here





linear-algebra matrix-equations





share|cite|improve this question










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asked Jul 25 at 12:21









belinda

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  • It is not true. For example, If $A=0$ and $B$ is a non-zero vector, then $det(A)=0$ and so are all the determinants $Delta_1,...Delta_4$. But the system $Ax=B$ has no solutions.
    – user578878
    Jul 25 at 12:30
















  • It is not true. For example, If $A=0$ and $B$ is a non-zero vector, then $det(A)=0$ and so are all the determinants $Delta_1,...Delta_4$. But the system $Ax=B$ has no solutions.
    – user578878
    Jul 25 at 12:30















It is not true. For example, If $A=0$ and $B$ is a non-zero vector, then $det(A)=0$ and so are all the determinants $Delta_1,...Delta_4$. But the system $Ax=B$ has no solutions.
– user578878
Jul 25 at 12:30




It is not true. For example, If $A=0$ and $B$ is a non-zero vector, then $det(A)=0$ and so are all the determinants $Delta_1,...Delta_4$. But the system $Ax=B$ has no solutions.
– user578878
Jul 25 at 12:30















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