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Theorem
Using Binomial theorem, prove that: ..
Using Binomial theorem, prove that: ..Theorem:
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B = C Hence the inverse..
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B = C Hence the inverse..Remainder Theorem
Remainder Theorem - Recall the Remainder theorem and the Factor theorem. When f(x) is divided by (x-a) the remainder is (x-a) and if the remainder f(a) = 0 then x - a is a factor of the expression f (x..
Remainder Theorem - Recall the Remainder theorem and the Factor theorem. When f(x) is divided by (x-a) the remainder is (x-a) and if the remainder f(a) = 0 then x - a is a factor of the expression f (x..De Moivre's Theorem
De Moivre's Theorem..
De Moivre's Theorem..De Moivre's Theorem
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometr..
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometr..Factor theorem
If p(x) is a polynomial in x and is divided by and the remainder = f(a) is zero then (x-a) is a factor of p(x..
Factor Theorem
If p(x), a polynomial in x is divided by x-a and the remainder = f (a) is zero, then (x-a) is a factor of p(x..
Remainder theorem
If f(x) is a polynomial in x and is divided by x-a; then the remainder is is the value of f(x) at x = a i.e., remainder = f(..
Factor Theorem
Statement - If p(x), a polynomial in x is divided by x-a and the remainder = f (a) is zero, then (x-a) is a factor of p(..
Applications of Binomial Theorem
Some Applications of Binomial Theorem for Fractional Index - If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximat..
Some Applications of Binomial Theorem for Fractional Index - If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximat..See what our Users say :
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