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/ Linear Algebra Terms
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Can you name the Linear Algebra Ultimate Review?
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nskogh
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Question
Answer
the set of all linear combinations of a set of vectors
A system is consistent if and only if the row rank of the coefficient matrix equals the row rank of the augmented matrix
using row operations to put a matrix into ref
vector of length one
0-parameter solution =
the number of vectors in a basis for a vector space
3-or more-parameter solution =
system where all constraints are 0 (when every equation in the system equals 0)
the distance between vector u and the projection of vector u onto vector v
x vector =(x1,x2,...,xn) = Po vector + t times the v vector
vector x = vector Po + t times vector v1 + s times vector v2
when you multiply this with a matrix it is like multiplying by one
when it costs less then $1 in raw materials to make $1 worth of product
vector v = c1v1+c2v2+...+ckvk for some scalars c1,c2...ck
vector starting at the origin and ending at a point
A^t (switching a matrix's rows and columns)
when a linear system has an infinite number of solutions it has:
If every vector is a unit vector and the vectors are mutually orthogonal then the vectors are
1-parameter solution =
an extra variable that's added to an inequality to make the constraint an equality
2-parameter solution =
A basis that is also an orthonormal set
a basic solution to a linear program in which all variables are nonnegative
Question
Answer
If given any demand there is a production schedule that meets that demand
choosing a point in a matrix, turning it into a one, then annihilating entries above and below it
vector u times vector v = u1v1+...+unvn
A vector space W that is part of a larger vector space V
when vector u times vector v = 0, U and v vectors are:
a matrix where all entries are non-negative and every column sums to one
the square root of (u1)^2+...+ (uk)^k
If AB = I and BA = I then B is the _______ of A.
the number of non-zero rows the matrix has after it has been put in ref
When no vector in S is a linear combination of the other vectors
If det(A) does not equal 0 then A is
method used to find the determinant and/or inverse of a 3x3 matrix or larger
Problem of maximizing or minimizing a linear function over a set of constraints
When vectors can be written as linear combinations of each other they are
If a set of vectors spans the vector space V and the set is linearly independent it is a
first nonzero entry in every row is one and below each one are zeroes
linear system that does not have any solutions
above and below leading ones are zeroes
Vector Sn = T^n times vector So
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
when one non-zero vector is a scalar multiple of another, these vectors are:
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