1992
... 17(c) For x = 1 there are 8 solutions; for x = 2 seven solutions; …, for x =8 one solution. Answer is 8+7+6+5+4+3+2+1. 18(b) Form a triangle OPQ where O is the center of the circle and P,Q are points on the circle, and A is the angle POQ. Draw an altitude PR from P to OQ. Then PR = sin A, ...
... 17(c) For x = 1 there are 8 solutions; for x = 2 seven solutions; …, for x =8 one solution. Answer is 8+7+6+5+4+3+2+1. 18(b) Form a triangle OPQ where O is the center of the circle and P,Q are points on the circle, and A is the angle POQ. Draw an altitude PR from P to OQ. Then PR = sin A, ...
14. The minimal polynomial For an example of a matrix which
... spanned by (1, 0, 0). But we already know that similar matrices have eigenspaces of the same dimension. So A0 , A1 and A2 are inequivalent matrices. In fact there is another way to see that these matrices are not similar. Definition 14.2. Let φ : V −→ V be a linear transformation. We say that φ is n ...
... spanned by (1, 0, 0). But we already know that similar matrices have eigenspaces of the same dimension. So A0 , A1 and A2 are inequivalent matrices. In fact there is another way to see that these matrices are not similar. Definition 14.2. Let φ : V −→ V be a linear transformation. We say that φ is n ...
solving polynomial equations by radicals31
... The aim of this project is to determine the solvability by radicals of polynomials of different degrees. Further, for polynomials which are solvable by radicals, the Galois- theoretic derivation of the general solution to the polynomial is sought. Where a degree k ≥ 5 polynomial is found to be insol ...
... The aim of this project is to determine the solvability by radicals of polynomials of different degrees. Further, for polynomials which are solvable by radicals, the Galois- theoretic derivation of the general solution to the polynomial is sought. Where a degree k ≥ 5 polynomial is found to be insol ...
Please show work. 1. (y-1)(y-7)=0 Hence, either of the factors can be
... It was so as finding factors of 44 such that their difference 20 was difficult. I found all the factors and manipulated to get factors such that their difference 20. I reduced it to x2+10x-11=0 and factors of 11 are 11 and 1 whose difference is 10 and solved the equation. ...
... It was so as finding factors of 44 such that their difference 20 was difficult. I found all the factors and manipulated to get factors such that their difference 20. I reduced it to x2+10x-11=0 and factors of 11 are 11 and 1 whose difference is 10 and solved the equation. ...
Name
... Breeders can supply the academy with at most 20 poodles and 15 Siberian huskies each year. Each poodle eats 2 lb of food per day and each dog eats 6 lb of food per day. Food supplies are restricted to at most 100 lb per day. A poodle requires 1,000 hours per year of training whereas a sled dog requi ...
... Breeders can supply the academy with at most 20 poodles and 15 Siberian huskies each year. Each poodle eats 2 lb of food per day and each dog eats 6 lb of food per day. Food supplies are restricted to at most 100 lb per day. A poodle requires 1,000 hours per year of training whereas a sled dog requi ...
PDF
... Fermat numbers 22 + 1 ; known prime only for n = 0, 1, 2, 3, 4 . Part of the interest in them is Fact (Gauss): A regular n-gon can be constructed by compass and straight-edge ⇔ n = 2k d where d is a product of distinct Fermat primes. So the fact that we know of only 5 Fermat primes means we only kno ...
... Fermat numbers 22 + 1 ; known prime only for n = 0, 1, 2, 3, 4 . Part of the interest in them is Fact (Gauss): A regular n-gon can be constructed by compass and straight-edge ⇔ n = 2k d where d is a product of distinct Fermat primes. So the fact that we know of only 5 Fermat primes means we only kno ...
Factorization
In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms.Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.