Linear Algebra Questions
Explore questions in the Linear Algebra category that you can ask Spark.E!
The null space of an m×n matrix is a subspace of R^m.
The set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of R^n.
If the transpose of A is not invertible, then A is also not invertible. (Yes/No/Maybe)
The column space of an m×n matrix is a subspace of R^m.
Two vectors are linearly dependent if and only if they are colinear.
If the linear transformation TA(x)=Ax is one-to-one, then the columns of A form a linearly dependent set. (Yes/No/Maybe)
Suppose A and B are invertible matrices. A^7 is invertible.
Let V be the subset of R^3 consisting of the vectors ⎡⎣a b c⎤⎦ with abc=0. V is a subspace of R^3 .
Let V be the subset of R^3 consisting of the vectors ⎡⎣a b c⎤⎦ with abc=0. V contains the zero vector.
If A^T is row equivalent to the n×n identity matrix, then the columns of A span R^n. (Yes/No/Maybe)
A square matrix with two identical columns can be invertible. (Yes/No/Maybe)
If A is invertible, then the equation Ax=b has exactly one solution for all b in R^n. (Yes/No/Maybe)
Suppose A and B are invertible matrices.(In−A)(In+A)=In−A^2.
For any matrix A, there exists a matrix B so that A+B=0.
For any matrices A and B, if the product AB is defined, then BA is also defined.
A homogeneous system is always consistent.
If A is an m×n matrix then A^TA and AA^T are both defined.
If x is a nontrivial solution of Ax=0, then every entry of x is nonzero.
If A is a 5×4 matrix, and B is a 4×3 matrix, then the entry of AB in the 3rd row / 4th column is obtained by multiplying the 3rd column of A by the 4th row of B.
Suppose A and B are invertible matrices. (A+B)^2=A^2+B^2+2AB.