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