A College Algebra
A College Algebra
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In our eReader you can find the full English version of the book. Read A College Algebra Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A College Algebra
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Begin by subtracting the third column from the first and second columns. Then take out the factor 2 (§ 312), subtract 3 times the first column from the third, and multiply out the result by § 406.
DETERMINANTS. 369 416. Factoring of Determinants. If a determinant van- ishes when for any element a we put another element b, then a — b ts a factor of the determinant.
For the expansion contains only positive integral powers of the several elements, and we can write ^ = A, -\-A, a + A^d' + A, a'-\-,... (1) where Aq, Ai, A^, A3, , are expressions which do not involve a, and will, consequently, remain unchanged when we put b for a.
Putting b for a, since A becomes by hypothesis, we obtain = ^0 + ^1^ + A, b' + A^b' + (2) Subtracting (2) from (1), we obtain A = A, (a-b) + A, (a' - b') + A^ia' - b') Since every one of the expressions a — b, d^ — 5^ a^ — b^, , contains a — 6 as a factor, a — b is & factor of A.
The theorem also holds true when a and b are not elements, provided a and b enter into the expansion in positive integral powers only.
What to read after A College Algebra?
You can find similar books in the "Read Also" column, or choose other free books by George Albert Wentworth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Begin by subtracting the third column from the first and second columns. Then take out the factor 2 (§ 312), subtract 3 times the first column from the third, and multiply out the result by § 406.
DETERMINANTS. 369 416. Factoring of Determinants. If a determinant van- ishes when for any element a we put another element b, then a — b ts a factor of the determinant.
For the expansion contains only positive integral powers of the several elements, and we can write ^ = A, -\-A, a + A^d' + A, a'-\-,... (1) where Aq, Ai, A^, A3, , are expressions which do not involve a, and will, consequently, remain unchanged when we put b for a.
Putting b for a, since A becomes by hypothesis, we obtain = ^0 + ^1^ + A, b' + A^b' + (2) Subtracting (2) from (1), we obtain A = A, (a-b) + A, (a' - b') + A^ia' - b') Since every one of the expressions a — b, d^ — 5^ a^ — b^, , contains a — 6 as a factor, a — b is & factor of A.
The theorem also holds true when a and b are not elements, provided a and b enter into the expansion in positive integral powers only.
What to read after A College Algebra?
You can find similar books in the "Read Also" column, or choose other free books by George Albert Wentworth to read onlineMoreLess
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