System of linear equations

In mathematics, a system of linear equations is a collection of one or more linear equations involving the same set of variables. For example, 3 x + 2 y − z = 1 2 x − 2 y + 4 z = − 2 − x + 1 2 y − z = 0 is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are satisfied. A solution to the system above is given by x = 1 y = − 2 z = − 2 since it makes all three equations valid; the word "system" indicates that the equations are to be considered collectively, rather than individually. In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject, used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, play a prominent role in engineering, chemistry, computer science, economics. A system of non-linear equations can be approximated by a linear system, a helpful technique when making a mathematical model or computer simulation of a complex system.

The coefficients of the equations are real or complex numbers and the solutions are searched in the same set of numbers, but the theory and the algorithms apply for coefficients and solutions in any field. For solutions in an integral domain like the ring of the integers, or in other algebraic structures, other theories have been developed, see Linear equation over a ring. Integer linear programming is a collection of methods for finding the "best". Gröbner basis theory provides algorithms when unknowns are polynomials. Tropical geometry is an example of linear algebra in a more exotic structure; the system of one equation in one unknown 2 x = 4 has the solution x = 2. However, a linear system is considered as having at least two equations; the simplest kind of nontrivial linear system involves two equations and two variables: 2 x + 3 y = 6 4 x + 9 y = 15. One method for solving such a system is. First, solve the top equation for x in terms of y: x = 3 − 3 2 y. Now substitute this expression for x into the bottom equation: 4 + 9 y = 15.

This results in a single equation involving only the variable y. Solving gives y = 1, substituting this back into the equation for x yields x = 3 / 2; this method generalizes to systems with additional variables A general system of m linear equations with n unknowns can be written as a 11 x 1 + a 12 x 2 + ⋯ + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + ⋯ + a 2 n x n = b 2 ⋮ a m 1 x 1 + a m 2 x 2 + ⋯ + a m n x n = b m


PrISUm Solar Car is the multidisciplinary student-run solar car racing team from Iowa State University that designs and builds solar powered vehicles to compete in the American Solar Challenge. The club was founded in 1989 by a group of engineering honor students from Tau Beta Pi and was known as the ISU Solar Car Project. In 1990, the team adopted the name of PrISUm. PrISUm Solar Car is a dedicated group of students committed to building a practical solar car that changes the paradigm of transportation. In doing so, they strive to inspire future generations to pursue their passions through STEAM education. Since 1989, Team PrISUm has built and raced 14 different cars and is one of only a handful of teams to have qualified and raced a new vehicle for every Sunrayce and American Solar Challenge races. Team PrISUm made the first solar car from the state of Iowa with its entrance in the 1990 GM Sunrayce USA. Team PrISUm consists of about 120 team members from the Iowa State University campus and welcomes students from all majors interested in working on any aspect of the diverse project.

The team has three distinct divisions that are each necessary for designing and teaching the public about solar cars. The Electrical Division is responsible for designing and building the battery system, solar array, power electronics and software for the car; the Mechanical Division is responsible for the design and fabrication of the outside shell of the vehicle and all the mechanical components for the car. The Business Division is responsible fundraising, project budgeting, outreach and media. 1990: ‘’PrISUm’’: GM Sunrayce USA: Placed 17 out of 34.

Percy Hurd

Sir Percy Angier Hurd was a British journalist and Conservative Party politician who served as a Member of Parliament for nearly thirty years. He was the first of four generations of Hurds to serve as Conservative MPs. Percy Hurd was the eldest son of his wife Elizabeth, he was editor of The Outlook, a weekly magazine published in London from 1898 to 1928. He became editor of the Canadian Gazette and London editor of the Montreal Star and other journals in Canada. During the First World War, he made various visits to the battle-front to study and record the work of the Canadian contingent, he was a member of the executive committee of the Agricultural Relief of Allies Fund, twice reported on the needs of the farmers in the provinces of France from which the Germans had been pushed back. Hurd was a fervent advocate of the British Empire, wrote several books on the subject, including one written jointly with his brother Archibald (later Sir Archibald Hurd, a naval critic, editor of the Naval and Military Record from 1896–1899 and a journalist with the Daily Telegraph until 1928.

Hurd was first elected to the House of Commons at the 1918 general election as the Coalition Conservative MP for the Frome division of Somerset. The seat had been held by the Liberal Party for all but nine of the preceding fifty years, but Hurd's possession of the "coalition coupon" issued to supporters of David Lloyd George's Liberal-Conservative coalition government combined with a strong showing from a Labour Party candidate allowed him to win the seat, ousting Sir John Barlow who had represented Frome since 1896. At the 1922 general election, Hurd faced only a Labour opponent, was re-elected with a modest majority of only 2.4% of the votes. However, at the 1923 general election, Frome was one of many seats won by the Labour Party. Hurd did not stand again at Frome, at the next general election in October 1924 he stood instead in the Devizes division of Wiltshire, a Conservative-leaning constituency, gained by the Liberals in 1923. Hurd took the seat with a majority of over 20% of the vote, remained as MP for Devizes until he retired from Parliament at the 1945 general election.

He was knighted in the 1932 King's Birthday Honours, "for political and public services". According to his grandson, Douglas Hurd, Percy "wasn't political, he used to go round villages in Wiltshire telling funny stories." In 1893 Percy married Hannah, daughter of Rev. William Jackson Cox, of Dundee, Angus and they had four children: Robert Philip Andrew Hurd, an architect who did not marry and had no children. Anthony Richard Hurd, a farmer and agricultural journalist who followed his father into politics and served as MP for Newbury from 1945 to 1964. Anthony was knighted in 1959 and became a life peer in 1964. Douglas William Hurd, a Captain in the Middlesex Regiment, killed in the First World War. Angier Percy Hurd, a Lieutenant in the Hertfordshire Regiment, killed during the German Spring Offensive in the First World War. Anthony's eldest son Douglas, was an MP from 1974 to 1997, rising to become Home Secretary and Foreign Secretary. Douglas's son, Nick has been the MP for Ruislip-Northwood since 2005.

Hurd, Percy Angier, ed.. People you know. Hurd, Percy Angier; the new empire partnership defence – commerce – policy. Hurd, Percy; the fighting territorials. Borden, Robert Laird, Sir. Percy Hurd; the war and the future, being a narrative compiled from speeches delivered at various periods of the war in Canada, the United States, Great Britain, with an introductory letter to the compiler, Percy Hurd. CS1 maint: multiple names: authors list Hurd, Percy. Canada past and future. Hurd, Percy; the Empire: a Family Affair. London: Philip Allan & Co. Hansard 1803–2005: contributions in Parliament by Sir Percy Hurd Portraits of Sir Percy Angier Hurd at the National Portrait Gallery, London