Linear Algebra Terms

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

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