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An elementary treatise on determinants; with their application to simultaneous linear equations and algebraical geometry, by Lewis Carroll
PDF Download An elementary treatise on determinants; with their application to simultaneous linear equations and algebraical geometry, by Lewis Carroll
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1867 Excerpt: ...are among them n--1 Equations, which have their F-Block not evanescent; and, when such a set of n--1 Equations is selected and taken along with each of the remaining Equations successively, each set of n Equations, so formed, has its i?-Block evanescent; the n+r Equations are consistent; (ch. III. Prop. VIII. Cor. their i?-Block is evanescent. (chap. III. Prop. XIII. Cor. Therefore, if there be, &c. Q. E. D. Proposition III. Th. If there be a Block, having one of its Minors of the kth degree, where k is less than the degree of a secondary Minor, not evanescent; and if, of the oblong Blocks formed from it by selecting k-t-1 of its longitudinals, each one, which contains that non-evanescent Minor, be evanescent: every other oblong Block, so formed, is evanescent. And the same is true of its laterals. Call the two dimensions of the Block 'm' and '�'. Let the Block be placed in either position, and let the k rows, and also the k columns, which contain the non-evanescent Minor, be placed first; and let each of the columns, except the last, be multiplied throughout by the symbol of a Variable; and let each row be equated to zero; and let the Equations, so formed, be represented by Prop. II. Thus, if, in the oblong Block J. e f g h V, it be given that (""Uo.md that _j k I m J' a b d 'bed efh =0, and I / g h j km k I m--0: the whole Block is evanescent. then the first � + 1 Equations contain m--1 Variables, and there are among them k Equations whose F-Block is not evanescent; and the iS-Block of these k +1 Equations is evanescent; First, let m--1 = k+; then the Equations are consistent; and the Variable xm_1 may have an arbitrary value assigned to it; and the /fc+ll01 Equation is dependent on the first k Equations; (ch. III. Prop. IX. also, ...
- Published on: 2012-05-19
- Original language: English
- Number of items: 1
- Dimensions: 9.69" h x .6" w x 7.44" l, .15 pounds
- Binding: Paperback
- 28 pages
About the Author
Lewis Carroll was the pen name of Charles Lutwidge Dodgson, an English writer, mathematician, Anglican deacon, and photographer. Best known for his classics Alice s Adventures in Wonderland, Through the Looking Glass, and Jabberwocky, Carroll was also an accomplished inventor who created an early version of what is today known as Scrabble. The publication of Alice s Adventures in Wonderland in 1865 brought Carroll a certain level of fame, although he continued to supplement his income through his work as a mathematics tutor at Christ Church, Oxford College. Carroll s whimsical characters and nonsensical verse resonated with Victorian-era readers, and his books continue to be enjoyed by numerous modern societies dedicated to his promoting his works.
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