Linear Algebra Terms

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

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Created Dec 14, 2011ReportNominate
Tags:algebra, linear, review, ultimate