Linear Algebra Definition
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Linear algebra definition. All of these denitions should be memorized and not just memorized but understood. What this means mathematically is that the function has either one or two variables with no exponents or powers. A linear equation is an algebraic equation such as y 4x 3 in which the variables are of the first degree that is raised only to the first power. Linear algebra definition is a branch of mathematics that is concerned with mathematical structures closed under the operations of addition and scalar multiplication and that includes the theory of systems of linear equations matrices determinants vector spaces and linear transformations. An equation that makes a straight line when it is graphed.
Two systems of linear equations in n unknowns are equivalent if they have the same set of solutions. Home math algebra what does linear mean in mathematics. A system of linear equations a x b is homogeneous if b 0. Of or resembling a line. Khan academy is a nonprofit with the mission of providing a free world class education for anyone anywhere.
Lets get our feet wet by thinking in terms of vectors and spaces. A linear function is any function that graphs to a straight line. Denitions of linear algebra terms in order to learn and understand mathematics it is necessary to understand the meanings of the terms vocabulary words that are used. Illustrated definition of linear equation. In mathematics linear refers to an equation or function that is the equation of a straight line and takes the form y mx b where m is equal to the slope and b is equal to the y intercept.
An arbitrary subset of a linear space like say a cantor set has nothing to do with linear algebra methods so the definition is made to exclude such things. The motivation for insisting on this is that when we want to do linear algebra we need things to be linear spaces. The graph of such an equation is a straight line.
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