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MATH Midterm One Def

TermDefinition
What is a line in R^2? Is a straight, 1-d figure that extends infinitely in two dimensions. Usually in the form ax+by=c
What is a linear equation in n variables? Is an algebraic equation that takes the form a1x1 + a2x2 + ... + an*xn = b.
What is a system of m linear equations in n variables? Is a collection of m equations which are in n variables.
What is a solution to a system of m linear equations in n variables? Are a set of values for the x variables that satisfy every equation in the system.
What is an augmented matrix for a system of m linear equations in n variables? An augmented matrix for this system is constructed by arranging the coefficients of the variables and the constants into a matrix.
What is a non-augment matrix? Is a matrix without the vertical bar that separates the coefficients of the variables and the constants.
What is the formula/definition for matrix addition? Is when two matrices of the same size are added, and are defined by matrix C= matrix A + matrix B.
What is the formula/definition for matrix multiplication? Cant explain here lmao
What is the n x n identity matrix In? Is a square matrix with n rows and n columns, that have ones on the diagonal from top left to bottom right with zeros everywhere else.
What is an inverse matrix for an n x n matrix A? Is an n x n square matrix that, when multiplied by A, produces the identity matrix. A^-1 * A = In.
What does it mean for a matrix to be invertible? It means that the matrix has an inverse.
What is a linear inequality in n variables? Is an inequality that involves linear combinations of the variables. Usually in the form: a1x1 + a2x2 + ... + anxn (> or <) b.
What is a system of m linear inequalities in n variables? Is a collection of m linear inequalities that each involve n variables.
What is a feasible set for a system of m linear inequalities in n variables? Is the set of points or vectors in space that satisfy every inequality.
Created by: calhouncouch
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