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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
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
1-parameter solution =
A basis that is also an orthonormal set
A vector space W that is part of a larger vector space V
A^t (switching a matrix's rows and columns)
the distance between vector u and the projection of vector u onto vector v
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:
above and below leading ones are zeroes
a matrix that represents the cost per dollar to run several companies/industries in an economy
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
the set of all linear combinations of a set of vectors
Vector Sn = T^n times vector So
0-parameter solution =
If every vector is a unit vector and the vectors are mutually orthogonal then the vectors are
first nonzero entry in every row is one and below each one are zeroes
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
when a linear system has an infinite number of solutions it has:
choosing a point in a matrix, turning it into a one, then annihilating entries above and below it
If a set of vectors spans the vector space V and the set is linearly independent it is a
Question
Answer
the square root of (u1)^2+...+ (uk)^k
system of linear equations with one or more solutions
vector u times vector v = u1v1+...+unvn
If det(A) does not equal 0 then A is
using row operations to put a matrix into ref
vector of length one
system where all constraints are 0 (when every equation in the system equals 0)
When vectors can be written as linear combinations of each other they are
vector v = c1v1+c2v2+...+ckvk for some scalars c1,c2...ck
when it costs less then $1 in raw materials to make $1 worth of product
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
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
the number of vectors in a basis for a vector space
an extra variable that's added to an inequality to make the constraint an equality
linear system that does not have any solutions
when vector u times vector v = 0, U and v vectors are:
2-parameter solution =
If given any demand there is a production schedule that meets that demand
a matrix where all entries are non-negative and every column sums to one
3-or more-parameter solution =
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,
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,
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