An Elementary Treatise On the Theory of Equations
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What reading level is An Elementary Treatise On the Theory of Equations book?
To quickly assess the difficulty of the text, read a short excerpt:
Let the given equations be aix' + bix" = k^ (1) a^' + b^x" = k. (2) a3x' + b, x" = k, (3) 56 THEORY OF EQUATIONS.
Art. 42 Since the above system is to be consistent, the values of the unknowns obtained by solving any two of the equations must satisfy the third equation.
Solving equations (^2) and (3), we get h.
b.
b.
k.
1 _ h h = - A^ h a. 2 b.
Ch ~h «3 hs «3 h a. 2 k2 «3 h a. 2 h «3 h S'ubstituting these values of x' and x" in equation (1), and reducing, we get «i b. 2 h -b 1 1 ^2 ^'2 + k.
ao ...b.
h ks 1, 1 «3 ks as 6 «i bi ki «2 &2 ^'2 = 0, «3 ^3 ^ 3 0, which is the condition of consistency of the three given equa- tions. For example, the system of equations 6a;'+ x" = — l, 5. X' -10 a;" = 5, 4. R'+ 3a;" =-7 is consistent, because we have = 0.
43. We shall now take up the general case, and investigate this relation in the case of {n + 1) linear equations involving n unknowns.
Consider the following system : Art. 43 APPLICATION. '^ OF DETERMINANTS.
57 a^x' + a, . R a. , 'x' + a.
What to read after An Elementary Treatise On the Theory of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Marx Barton to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Let the given equations be aix' + bix" = k^ (1) a^' + b^x" = k. (2) a3x' + b, x" = k, (3) 56 THEORY OF EQUATIONS.
Art. 42 Since the above system is to be consistent, the values of the unknowns obtained by solving any two of the equations must satisfy the third equation.
Solving equations (^2) and (3), we get h.
b.
b.
k.
1 _ h h = - A^ h a. 2 b.
Ch ~h «3 hs «3 h a. 2 k2 «3 h a. 2 h «3 h S'ubstituting these values of x' and x" in equation (1), and reducing, we get «i b. 2 h -b 1 1 ^2 ^'2 + k.
ao ...b.
h ks 1, 1 «3 ks as 6 «i bi ki «2 &2 ^'2 = 0, «3 ^3 ^ 3 0, which is the condition of consistency of the three given equa- tions. For example, the system of equations 6a;'+ x" = — l, 5. X' -10 a;" = 5, 4. R'+ 3a;" =-7 is consistent, because we have = 0.
43. We shall now take up the general case, and investigate this relation in the case of {n + 1) linear equations involving n unknowns.
Consider the following system : Art. 43 APPLICATION. '^ OF DETERMINANTS.
57 a^x' + a, . R a. , 'x' + a.
What to read after An Elementary Treatise On the Theory of Equations?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Marx Barton to read onlineMoreLess
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