LINEAR ALGEBRA FINAL TEST (T/F) QUESTIONS AND ANSWERS

LINEAR ALGEBRA FINAL TEST (T/F)
QUESTIONS AND ANSWERS
If two augmented matrices are row equivalent, they must have the same solution set -
Answer-True

The linear system, Ax=b has infinitely many solutions if the echelon form of A has fewer
nonzero rows than variables - Answer-False

Span{v1,...,vp} always contains the zero vector - Answer-True

If the column vectors of A span Rm. Then for any vector b in Rm, the system Ax = b is
consistent - Answer-True

A homogeneous system is always consistent - Answer-True

The equation Ax = 0 has the trivial solution if and only if the equation has at least one
free variable - Answer-False

If A has a pivot in each row, then the columns of A must be linearly independent -
Answer-False

If A is 2x3 then the domain of the transformation x to Ax is R3 and the range is R2 -
Answer-False, The domain is R3, but the range might be either R2 or R1 if the vectors
are dependent

The columns of an invertible matrix Anxn form a basis of Rn - Answer-True

The Amxn has m pivots, then Col A = Rm - Answer-True

The columns of A are linearly independent if Nul A = {0} - Answer-True

The number of vectors in a basis of Col A equals the number of pivots of A - Answer-
True

A linearly independent set in R5 cannot have more than 5 vectors - Answer-True

The solution set of Ax = 0 forms a subspace of Rn if A is mxn - Answer-True

Col A is the set of all vectors that can be written as Ax for some x - Answer-True

If A is mxn, then Col A is a subspace of Rn - Answer-False

If H = Span{v1,...,vp}, then {v1,...,vp} is a basis for H - Answer-False