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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 )
linear-algebra matrix-equations
asked Jul 25 at 12:21
belinda
187
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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 )
linear-algebra matrix-equations
asked Jul 25 at 12:21
belinda
187
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
add a comment |Â
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 )
linear-algebra matrix-equations
asked Jul 25 at 12:21
belinda
187
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 )
linear-algebra matrix-equations
asked Jul 25 at 12:21
belinda
187
asked Jul 25 at 12:21
belinda
187
asked Jul 25 at 12:21
belinda
187
asked Jul 25 at 12:21
belinda
187
187
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
add a comment |Â
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
add a comment |Â
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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