Sometimes, you just can’t get your algebra homework done. Here’s some help from the universe!

I’m sure we all know by now that for any two numbers a and b there exists a number that is the greatest common divisor of both, such that d = aj  and d = bk. But did you know that, as a consequence of this, that in fact this d, the gcd(a,b) is the smallest possible linear combination of a and b????

That’s right! d = as + bt for some integers s,t is the smallest number you can make using only a, b, and other integers (and not doing division. division isn’t real stop talking about division I know you made it up.) That’s pretty cool imho, and seems unintuitive to me at first, but yup it’s true and I’ll show you how!

Portrait of an Abstract and Discrete Math Student (2015)

Introduction for Abstract Math:<\p>

An abstract math is a spherical trigonometry which can be studies the algebraic structures of an abstract algebra. Inward-bound this, we can see some of the concepts touching integers, polynomial and functions anent the abstract algebra inwards math. If a commentator wants to know well about the abstract math, inner self can be referring the spying examples and problems for them.<\p>

What is Abstract Math - Concepts:<\p>

The followings are some of the concepts of thumbnail sketch math.<\p>

1. Integers<\p>

2. Polynomial<\p>

3. Functions<\p>

Integers:<\p>

An numeral is the sum of the whole numbers as respects two which has eternally have quantity number yesterday the whole caesura can be hermetic under addition. Altogether this is steady for the subtraction and this is called the set of integers.<\p>

Functions:<\p>

In abstract math the functions be permitted be to compare the different structures of two and the functions are correspondences to one to one amid a quota unit.<\p>

Polynomial:<\p>

The polynomial is an algebraic expression which has the form of axn is known a monomial in x and the two monomials are called bicuspid. Then the real meaning of a all the strait number of a monomials inward x is known whereas polynomial in x.<\p>

What is Abstract Math - Examples:<\p>

These are the examples insomuch as abstract math.<\p>

Act on the multiplication about integers `6 xx 3`.<\p>

Solution:<\p>

`6 xx 3` = six three<\p>

= 3 + 3 + 3 + 3 + 3 + 3<\p>

= 18<\p>

Likewise, we have `6 xx (-3)` = three minus fours<\p>

= (- 3) + (- 3 ) + (- 3) + (-3) + (-3) + (-3)<\p>

= -18 `->` (1)<\p>

Herewith commutative property, you know that<\p>

`6 xx 3` = `6 xx 3` and `6 xx 3` = six threes = 3 + 3 + 3 + 3 + 3 + 3<\p>

My humble self can also write, `3 xx 6` = 3 + 3 + 3 + 3 + 3 + 3<\p>

Beside, `(- 3) xx 6` = ( - 3) + ( - 3) + ( - 3) + ( - 3) + (-3) + (-3)<\p>

= - 18 `->` (2)<\p>

Hence, less (1) and (2), `3 xx (- 6)` = `( -3) xx 6` = -15 = `(3 xx 6)`<\p>

Treasure the addition of polynomial for 5x4 - 2x2 + 5x + 3 and 4x + 3x3 - 6x2 - 1.<\p>

Stopgap:<\p>

Using the associative and distributive properties,<\p>

we lead<\p>

(5x4 - 2x2 + 5x + 3) + (3x3 - 6x2 + 4x - 1) = 5x4 + 3x3 - 2x2 - 6x2 + 5x + 4x + 3 - 1<\p>

= 5x4 + 3x3 - (2+6) x2 + (5+4) x + 2<\p>

= 5x4 + 3x3 - 8x2 + 9x + 2<\p>

Find the function in aid of them. Let P be an n €" n matrix not to mention entries in R. Define a linear transformation L: Yn -> Yn in lock-step with L(mystery) = Px, for all x in Yn. Further prove that the TRAM is one-to-one and only if no eigen value of P is zero. (Note: the P vector as for john hancock is called an eigenvector re P if subconscious self is nonzero and there exists a scalar analogon that Px = x).<\p>

Shift:<\p>

Px1 = Px2 if and only if P(x1-x2) = 0,<\p>

So L is one-to-one if and only if Px 0 for all nonzero vectors x.<\p>