The leading coefficient of the first row is 1; 2 is the leading coefficient of the second row; 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.
42.
Which means that the non-leading coefficients of the quotient are all divisible by; the remaining verification that the constant term of the quotient is can be done by substituting ( instead of ) for into the expanded form.
43.
The last expression shows that for fixed source dimension " n, " the target dimension is a polynomial in " d " of degree " n " and leading coefficient 1 / n !.
44.
As can be observed by first performing long division with such a non-monic divisor, the coefficients of f ( x ) are divided by the leading coefficient of g ( x ) after " dropping ", and before multiplying.
45.
Once all of the leading coefficients ( the left-most non-zero entry in each row ) are 1, and every column containing a leading coefficient has zeros elsewhere, the matrix is said to be in reduced row echelon form.
46.
Once all of the leading coefficients ( the left-most non-zero entry in each row ) are 1, and every column containing a leading coefficient has zeros elsewhere, the matrix is said to be in reduced row echelon form.
47.
In the following computation " deg " stands for the degree of its argument ( with the convention deg ( 0 ) < 0 ), and " lc " stands for the leading coefficient, the coefficient of the highest degree of the variable.
48.
The other definition, which is mentioned in the previous section, is that the degree of " X " is the leading coefficient of the Hilbert polynomial of " X " times ( dim " X " ) !.
49.
It is in echelon form because the zero row is at the bottom, and the leading coefficient of the second row ( in the third column ), is to the right of the leading coefficient of the first row ( in the second column ).
50.
It is in echelon form because the zero row is at the bottom, and the leading coefficient of the second row ( in the third column ), is to the right of the leading coefficient of the first row ( in the second column ).
