Linear Algebra Terms

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

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