Mixing
defining the determinant of a matrix combined of function
0
$begingroup$
I have the following question:
f1(x),....fn(x) belong to polynomial space with a degree less or equal to n-2
a1,....an belong to the real numbers.
what is the determinant of matrix A ?
determinant
edited Jan 12 at 18:32
angryavian
40.9k23380
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
$endgroup$
add a comment |
0
$begingroup$
I have the following question:
f1(x),....fn(x) belong to polynomial space with a degree less or equal to n-2
a1,....an belong to the real numbers.
what is the determinant of matrix A ?
determinant
edited Jan 12 at 18:32
angryavian
40.9k23380
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
$endgroup$
$begingroup$
Hint: The rows of your matrix are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 18:35
$begingroup$
can you please add more?
$endgroup$
– KIMKES1232
Jan 12 at 19:42
$begingroup$
The polynomials of degree $leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 19:48
$begingroup$
thank you! great
$endgroup$
– KIMKES1232
Jan 12 at 20:28
add a comment |
0
0
0
$begingroup$
I have the following question:
f1(x),....fn(x) belong to polynomial space with a degree less or equal to n-2
a1,....an belong to the real numbers.
what is the determinant of matrix A ?
determinant
edited Jan 12 at 18:32
angryavian
40.9k23380
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
$endgroup$
I have the following question:
f1(x),....fn(x) belong to polynomial space with a degree less or equal to n-2
a1,....an belong to the real numbers.
what is the determinant of matrix A ?
determinant
determinant
edited Jan 12 at 18:32
angryavian
40.9k23380
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
edited Jan 12 at 18:32
angryavian
40.9k23380
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
edited Jan 12 at 18:32
angryavian
40.9k23380
edited Jan 12 at 18:32
angryavian
40.9k23380
edited Jan 12 at 18:32
angryavian
40.9k23380
40.9k23380
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
asked Jan 12 at 18:29
KIMKES1232KIMKES1232
11
11
$begingroup$
Hint: The rows of your matrix are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 18:35
$begingroup$
can you please add more?
$endgroup$
– KIMKES1232
Jan 12 at 19:42
$begingroup$
The polynomials of degree $leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 19:48
$begingroup$
thank you! great
$endgroup$
– KIMKES1232
Jan 12 at 20:28
add a comment |
$begingroup$
Hint: The rows of your matrix are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 18:35
$begingroup$
can you please add more?
$endgroup$
– KIMKES1232
Jan 12 at 19:42
$begingroup$
The polynomials of degree $leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 19:48
$begingroup$
thank you! great
$endgroup$
– KIMKES1232
Jan 12 at 20:28
$begingroup$
Hint: The rows of your matrix are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 18:35
$begingroup$
Hint: The rows of your matrix are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 18:35
$begingroup$
can you please add more?
$endgroup$
– KIMKES1232
Jan 12 at 19:42
$begingroup$
can you please add more?
$endgroup$
– KIMKES1232
Jan 12 at 19:42
$begingroup$
The polynomials of degree $leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 19:48
$begingroup$
The polynomials of degree $leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 19:48
$begingroup$
thank you! great
$endgroup$
– KIMKES1232
Jan 12 at 20:28
$begingroup$
thank you! great
$endgroup$
– KIMKES1232
Jan 12 at 20:28
add a comment |
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$begingroup$
Hint: The rows of your matrix are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 18:35
$begingroup$
can you please add more?
$endgroup$
– KIMKES1232
Jan 12 at 19:42
$begingroup$
The polynomials of degree $leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent.
$endgroup$
– darij grinberg
Jan 12 at 19:48
$begingroup$
thank you! great
$endgroup$
– KIMKES1232
Jan 12 at 20:28