The Principles of Elementary Algebra |
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Page 300
... matrix . And it is readily seen from the principles of Art . 252 , that the interchange of any two rows , or of any two columns in a matrix changes the sign of the matrix , since it increases or decreases the number of inversions in the ...
... matrix . And it is readily seen from the principles of Art . 252 , that the interchange of any two rows , or of any two columns in a matrix changes the sign of the matrix , since it increases or decreases the number of inversions in the ...
Page 302
... matrix of the third order ; in practice the portion with- out the matrix is not written , the operation being carried on mentally . Ex . 1 . Ex . 2 . 247 1 2 12.2.6 +4.1.3 + 7.1.5 −3.2.7 356 -2.5.1 1.4.6 5 . 147 5 81.5.9 + 2.6.7 + 3.4 ...
... matrix of the third order ; in practice the portion with- out the matrix is not written , the operation being carried on mentally . Ex . 1 . Ex . 2 . 247 1 2 12.2.6 +4.1.3 + 7.1.5 −3.2.7 356 -2.5.1 1.4.6 5 . 147 5 81.5.9 + 2.6.7 + 3.4 ...
Page 303
... matrices of the third order , and then expand these . ) x 1 x 1 3. Show that x 1 1 x = x ( 1 − x ) 3 . x 1 1 1 260. We see from the preceding article that as soon as a matrix is reduced to depend upon matrices of the third order , we ...
... matrices of the third order , and then expand these . ) x 1 x 1 3. Show that x 1 1 x = x ( 1 − x ) 3 . x 1 1 1 260. We see from the preceding article that as soon as a matrix is reduced to depend upon matrices of the third order , we ...
Page 304
... matrix with p written for a , the matrix with q written for a . And the matrix thus becomes the sum of two matrices of the same order . 231 Ex . 1 . 521 - 34 1 1 + 1 31 +121 2 + 1 41 1 3 1 1 3 1 1 3 1 4 2 1 + 1 21 241 - 421 = 4 , 14 1 ...
... matrix with p written for a , the matrix with q written for a . And the matrix thus becomes the sum of two matrices of the same order . 231 Ex . 1 . 521 - 34 1 1 + 1 31 +121 2 + 1 41 1 3 1 1 3 1 1 3 1 4 2 1 + 1 21 241 - 421 = 4 , 14 1 ...
Page 305
... matrix will vanish after dividing by 2 . 263. Let a1 be changed to a + nb1 , ɑ2 to ɑ2 + nb2 , as to ag + nbs , etc. , throughout the a - column ; and let the value of the new matrix be noted by D ' . Then D ' = ( a1 + nb1 ) A1 − ( ɑ2 + ...
... matrix will vanish after dividing by 2 . 263. Let a1 be changed to a + nb1 , ɑ2 to ɑ2 + nb2 , as to ag + nbs , etc. , throughout the a - column ; and let the value of the new matrix be noted by D ' . Then D ' = ( a1 + nb1 ) A1 − ( ɑ2 + ...
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a₁ ab˛ arithmetic ax˛ b₁ becomes binomial binomial theorem c₁ coefficients complete square continued fraction convergent cube root decimal denominator denote diagonal difference dimensions Divide divisor elementary algebra equal equate coefficients equation EXERCISE expansion expression find the L. C. M. find the nth Find the value finite geometric geometric series given gives graph Hence imaginary independent term integer integral function inversions letters linear factors logarithms mantissa matrix miles monomial Multiply negative nth root nth term number of terms numerical quantity operation permutations positive integers proper fraction quadratic quantitative symbol R₁ rationalizing factor recurring series relation remainder result sides signs Similarly solution square root substituting subtract suffixes surd theorem tion triangle U₂ variable Whence zero
Popular passages
Page 90 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 254 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 336 - ... University of Ohio, of Pennsylvania, of Michigan, of Wisconsin, of Kansas, of California, of Missouri, Stanford University, etc., etc. "Those acquainted with Mr. Smith's text-books on conic sections and solid geometry will form a high expectation of this work, and we do not think they will be disappointed. Its style is clear and neat, it gives alternative proofs of most of the fundamental theorems, and abounds in practical hints, among which we may notice those on the resolution of expressions...
Page 254 - ... that the logarithm of the product of two numbers is the sum of the logarithms of the numbers.
Page 74 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.