Mixing
Linear algebra: Finding the number of parameters of a system given dimensions and rank
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Suppose the system Ax = b is consistent and A is a 6 x 7 matrix and rank(A) = 2. How many parameters does the system have?
linear-algebra
asked Apr 2 '16 at 6:13
user298519user298519
1155
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add a comment |
$begingroup$
Suppose the system Ax = b is consistent and A is a 6 x 7 matrix and rank(A) = 2. How many parameters does the system have?
linear-algebra
asked Apr 2 '16 at 6:13
user298519user298519
1155
$endgroup$
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The only thing you have to do is to calculate the number of free variables. If $n$ is the number of variables, then $n - r$ is the number of free variables, where $r$ is the rank of the matrix.
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– thanasissdr
Apr 2 '16 at 7:03
add a comment |
$begingroup$
Suppose the system Ax = b is consistent and A is a 6 x 7 matrix and rank(A) = 2. How many parameters does the system have?
linear-algebra
asked Apr 2 '16 at 6:13
user298519user298519
1155
$endgroup$
Suppose the system Ax = b is consistent and A is a 6 x 7 matrix and rank(A) = 2. How many parameters does the system have?
linear-algebra
linear-algebra
asked Apr 2 '16 at 6:13
user298519user298519
1155
asked Apr 2 '16 at 6:13
user298519user298519
1155
asked Apr 2 '16 at 6:13
user298519user298519
1155
asked Apr 2 '16 at 6:13
user298519user298519
1155
asked Apr 2 '16 at 6:13
user298519user298519
1155
1155
$begingroup$
The only thing you have to do is to calculate the number of free variables. If $n$ is the number of variables, then $n - r$ is the number of free variables, where $r$ is the rank of the matrix.
$endgroup$
– thanasissdr
Apr 2 '16 at 7:03
add a comment |
$begingroup$
The only thing you have to do is to calculate the number of free variables. If $n$ is the number of variables, then $n - r$ is the number of free variables, where $r$ is the rank of the matrix.
$endgroup$
– thanasissdr
Apr 2 '16 at 7:03
$begingroup$
The only thing you have to do is to calculate the number of free variables. If $n$ is the number of variables, then $n - r$ is the number of free variables, where $r$ is the rank of the matrix.
$endgroup$
– thanasissdr
Apr 2 '16 at 7:03
$begingroup$
The only thing you have to do is to calculate the number of free variables. If $n$ is the number of variables, then $n - r$ is the number of free variables, where $r$ is the rank of the matrix.
$endgroup$
– thanasissdr
Apr 2 '16 at 7:03
add a comment |
1 Answer
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Since rank is the no of non zero rows, so there will be 4 zero rows (no of rows are 6, rank is 2, another 4 are zero rows). Each zero row represent 1 parameter. Therefore there will be 4 parameters. Consistent means either many sol or unique sol
answered Oct 23 '17 at 15:21
MeenMeen
1
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1 Answer
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$begingroup$
Since rank is the no of non zero rows, so there will be 4 zero rows (no of rows are 6, rank is 2, another 4 are zero rows). Each zero row represent 1 parameter. Therefore there will be 4 parameters. Consistent means either many sol or unique sol
answered Oct 23 '17 at 15:21
MeenMeen
1
$endgroup$
add a comment |
$begingroup$
Since rank is the no of non zero rows, so there will be 4 zero rows (no of rows are 6, rank is 2, another 4 are zero rows). Each zero row represent 1 parameter. Therefore there will be 4 parameters. Consistent means either many sol or unique sol
answered Oct 23 '17 at 15:21
MeenMeen
1
$endgroup$
add a comment |
$begingroup$
Since rank is the no of non zero rows, so there will be 4 zero rows (no of rows are 6, rank is 2, another 4 are zero rows). Each zero row represent 1 parameter. Therefore there will be 4 parameters. Consistent means either many sol or unique sol
answered Oct 23 '17 at 15:21
MeenMeen
1
$endgroup$
Since rank is the no of non zero rows, so there will be 4 zero rows (no of rows are 6, rank is 2, another 4 are zero rows). Each zero row represent 1 parameter. Therefore there will be 4 parameters. Consistent means either many sol or unique sol
answered Oct 23 '17 at 15:21
MeenMeen
1
answered Oct 23 '17 at 15:21
MeenMeen
1
answered Oct 23 '17 at 15:21
MeenMeen
1
answered Oct 23 '17 at 15:21
MeenMeen
1
1
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$begingroup$
The only thing you have to do is to calculate the number of free variables. If $n$ is the number of variables, then $n - r$ is the number of free variables, where $r$ is the rank of the matrix.
$endgroup$
– thanasissdr
Apr 2 '16 at 7:03