Linear Algebra Terms

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vector u times vector v = u1v1+...+unvn
0-parameter solution =
A basis that is also an orthonormal set
system where all constraints are 0 (when every equation in the system equals 0)
a matrix where all entries are non-negative and every column sums to one
x vector =(x1,x2,...,xn) = Po vector + t times the v vector
1-parameter solution =
2-parameter solution =
linear system that does not have any solutions
vector starting at the origin and ending at a point
A system is consistent if and only if the row rank of the coefficient matrix equals the row rank of the augmented matrix
A vector space W that is part of a larger vector space V
when it costs less then $1 in raw materials to make $1 worth of product
using row operations to put a matrix into ref
If det(A) does not equal 0 then A is
when a linear system has an infinite number of solutions it has:
If given any demand there is a production schedule that meets that demand
3-or more-parameter solution =
the distance between vector u and the projection of vector u onto vector v
vector x = vector Po + t times vector v1 + s times vector v2
Vector Sn = T^n times vector So
when one non-zero vector is a scalar multiple of another, these vectors are:
Problem of maximizing or minimizing a linear function over a set of constraints
the number of non-zero rows the matrix has after it has been put in ref
If a set of vectors spans the vector space V and the set is linearly independent it is a
If AB = I and BA = I then B is the _______ of A.
when you multiply this with a matrix it is like multiplying by one
system of linear equations with one or more solutions
vector v = c1v1+c2v2+...+ckvk for some scalars c1,
an extra variable that's added to an inequality to make the constraint an equality
choosing a point in a matrix, turning it into a one, then annihilating entries above and below it
first nonzero entry in every row is one and below each one are zeroes
When vectors can be written as linear combinations of each other they are
A^t (switching a matrix's rows and columns)
the set of all linear combinations of a set of vectors
When no vector in S is a linear combination of the other vectors
when vector u times vector v = 0, U and v vectors are:
the square root of (u1)^2+...+ (uk)^k
vector of length one
If every vector is a unit vector and the vectors are mutually orthogonal then the vectors are
the number of vectors in a basis for a vector space
a matrix that represents the cost per dollar to run several companies/industries in an economy
method used to find the determinant and/or inverse of a 3x3 matrix or larger
a basic solution to a linear program in which all variables are nonnegative
above and below leading ones are zeroes

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Created Dec 14, 2011ReportNominate
Tags:algebra, linear, review, ultimate