Space, the Final Frontier
The null space of an invertible matrix
What is just the zero vector?
A basis for the subspace of vectors [[x],[y],[z]] satisfying y=0 .
What is
{[[1],[0],[0]] ;[[0],[0],[1]]}?
Campus Clone
What is Column Space?
An eigenvalue for a non-invertible matrix
What is zero?
The number of solutions to the system
3x1+5x2-8x3+2x4=0
5x1-4x2+6x3-9x4=0
2x1+9x2+5x3+x4=0
What is infinity?
The conditions for a subset of \mathbb R^n to be a subspace
What are closed under vector addition, closed under scaling, and containing the zero vector?
The number of vectors in any basis for the column space of an invertible 3 by 3 matrix.
What is 3?
Covert Genie
What is Eigenvector?
They must be, if they are eigenvectors for distinct eigenvalues
What is linearly independent?
The number of solutions to the system
3x1+5x2-8x3 = 2
-4x2+6x3 = 9
5x3 = 5
What is one?
A basis for the null space of the matrix [[1,1]]
What is
{[[1],[-1]]}?
A geometric description of the subspace with basis vectors [[1],[1],[1]] and [[1],[2],[3]]
What is a plane through the origin in \mathbb R^3 ?
Alien Tiled Penny Nerd
What is Linearly Independent?
A matrix for which every vector in \mathbb R^4 is an eigenvector with eigenvalue 5.
What is 5I4?
The matrix that makes it easy to solve
Ax=b_1, Ax=b_2, ..., Ax=b_k
What is A^{-1} ?
This is a geometric description of the subspace of \mathbb R^3 spanned by [[1],[1],[1]], [[2],[2],[2]],and [[-5],[-5],[-5]]
What is a line through the origin?
The number of vectors in a basis for the subspace of \mathbb R^4 consisting of solutions to the equation 2x_1+4x_2 = 3x_3-x_4.
What is three?
Mr. Foxtrot's Mania Train
What is Matrix Transformation?
The eigenvalues of the matrix [[1 ,1],[1,1]]
What are 2 and 0?
One solution to a homogeneous system of 7 equations in 5 unknowns.
What is (0,0,0,0,0)?
Given some vector \mathbf v in \mathbb R^5, the possibilities for the subspaceW={A\mathbf v \text{ for all possible }3\times 5\text{ matrices }A}
What are {\mathbf 0} and \mathbb R^3 ?
A vector subspace of \mathbb R^4 that has no basis
What is
{[[0],[0],[0],[0]]}?
Thin Limo Vertebrate Remix
What is Invertible Matrix Theorem
A[[1],[2],[3]] when [[1],[1],[1]] is an eigenvector of A with
eigenvalue 2 and [[0],[1],[2]] is an eigenvector of A with
eigenvalue 3
What is
[[2],[5],[8]]?
Unfortunately, no one can be told what it is. You have to see it for yourself.
What is the matrix?