In row reduction, we can multiply a row by any real number.

If a linear system has no free variables, then it has an unique solution

If a matrix is in reduced row echelon form, then it is also in row echelon form.

Every matrix has a unique row echelon form.

A homogeneous linear system is always consistent

If a system Ax=b has more than one solution, then the system Ax=0 also has more than one solution.

The span of any two vectors in R² is R².

Let a, b, c, d be vectors in Rn. If {a, b, c, d} is linearly dependent, then {a, b, c} is also linearly dependent.

If {u, v, w} is linearly independent, then u, v, w are not in R².

Let u and v be vectors, -u is in the span of u and v.

All linear transformations map the zero vector to itself.

If T is a linear map from Rn to Rm, the corresponding matrix A is of size nxm

If a linear transformation is onto, it is not one-to-one.

Let A and C be matrices. If AC = 0, then either A=0 or C=0

If AB = I (identity matrix), then A is invertible

I will do good on this midterm