True or false Flashcards
If AB=C and C has 3 columns, then A has 3 columns.
False
A change-of-coordinates matrix is always invertible.
True
If A is m x n and the linear transformation x → Ax is onto, the rank A = m.
True
If A and B are n x n, then (A+B)(A-B) = A^2-B^2.
False
If AB = I, then A is invertible
False. A is not necessarily to be square.
If eqation Ax = b has at least one solution for each b in R^n, then the solution is unique for each b.
False. Not necessary to be square.
If two rows of a 3 x 3 matrix A are the same, then A is not invertible.
True.
A vector space is infinite-dimensional if it is spanned by an infinite set.
False.
If n x n matrices A and B have property AB = I, then AB = BA.
True.
If A is invertible and AB=BA, then A^-1B = BA^-1.
True.
Each elementary matrix is invertible.
True.
An elementary n x n matrix has either n or n+1 nonzero entries.
True.
Suppose that A is an n x n matrix. If the columns of A span R^n, then the columns are linearly independent.
True.
All solutions of a homogeneous system of 10 linear equations in 12 variables are multiples of one fixed nonzero solution.
False.
A nonhomogeneous system of 7 linear equations in 6 variables has a unique solution for every right-hand side.
False.
