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