Here is a linear equation in two variables: 2x+4y−31=123

Answer:

y=−11x+77/2

Step-by-step explanation:

The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]

Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.

The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]

In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.

Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C}  have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H}  of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.

Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]

Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]

The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.

The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]

Vector spaces

Main article: Vector space

Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.

A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]

Ms. Brown spent $5.25 on groceries and 75¢ on candies. What is the ratio of: a) cost of groceries to cost of candies b) cost of candies to total cost

9b-27= 3(2b-8)+2b solve for b


please show work on how you found b

Can someone please tell me the answer

DAY 5: 10/28-29/21
8.6.7
21. On a farm, a pigpen is 35 yards from a chicken coop, the chicken coop is 60 yards from a cow
pasture, and the distance between the pigpen and the cow pasture is 95 yards. Which
statement is true?
A
The distances between the pigpen, chicken coop, and cow pasture do not form a right
triangle because 35 + 60 # 95.
B
The distances between the pigpen, chicken coop, and cow pasture do not form a right
triangle because 352 + 602 7952.
The distances between the pigpen, chicken coop, and cow pasture form a right triangle
because 35 + 60 = 95.
с
D
The distances between the pigpen, chicken coop, and cow pasture form a right triangle
because 352 + 602 = 952.

Which shape does our galaxy have?(1 point)
circular

spiral

irregular

elliptical

HELP

Convert log xy = 1/2 to exponential form

a. x^y=1/2

b. y^x=1/2

c. square root of x=y

d. square root of y=x

Multiply (x + 1)^3
(x + 1)^3 = (x + 1)(x + 1)^2
= (x + 1)(x^2 + 2x + 1)
= x^3 +_____ x^2 +_____ x + _____

let (3x+24) represent the measure of a right angle. what are the possible values of x?​

1p
Oliver paid $21 for 6 t-shirts. Each shirt was the same price. What was the
cost of 1t-shirt?
$2.00
$2.50
$3.00
$3.50

the difference of complementary angles is 10 degree. find the measures of the angles.​

You pull horizontally on a 50-kg crate with a force of 450 n and the friction force on the crate is 250 n. the acceleration of the crate is​

Find the slope of the line that passes through (1, 2) and (10, 10).

Find the y-intercept of the following equation. Simplify your answer.
y
=
–2
x
+
4
5

How do you turn a whole number into a fraction

Pls help!!!!!!!!!!!!

I will give you brainliest if you solve the math question

GIVING BRAINLIST!!! SHORT QUESTION PLS ANSWER

Algerbra, pls answer fasttttttt

There is a raffle at a hockey game and 125 tickets are sold. Maris bought 3 tickets. What percent of the tickets
does Maris have?

PLEASE PLEASE PLEASEEEEEEE HELP RNNN xddddddd

please help me thanks​

De'shawn pays $8.16 for 12 pounds of sugar what is the price per pound of sugar asp

[tex]\sqrt3+2\sqrt2 - \sqrt6-4\sqrt2[/tex]

Several years ago, Winston invested in some gold. Gold is currently valued at $546 per ounce, which is 30% more than Winston originally paid for it. What was the purchase price of the gold?

HELP ASAP

Explains how to evaluate the expression 4x+10 for x=5.

Make a 4-by-4 logic grid on your own paper. Use it to help solve the logic
puzzle and answer the question.
A barbershop, a coffee shop, a flower shop, and a nail salon each have a sign
of a different color: blue, green, red, or purple (but not necessarily in that
order)
The coffee shop and the barbershop are next to the shop with the green sign.
The nail salon is not next to any of the other shops.
The barbershop's sign is either blue or red.

The store with the purple sign is next to the store with the green sign.
Which shop has the purple sign?
A. The coffee shop
B. The flower shop
C. The nail salon
D. The barbershop

-6/1 x - 3/5 divided by -0.25

Find the value of X.

Which climate zone generally receives the least amount of the
sun's energy?
a) tropical zone
b) subtropical zone
c) temperate zone
d) subpolar zone

What is the value of h?

h = 20
h = 35
h = 55
h = 70