If B₁, B₂ are bases for a given subspace, and A is the change of basis matrix from B₁ to B₂, then A is invertible, and
is the change of basis matrix from B₂ to B₁.

Question

If B₁, B₂ are bases for a given subspace, and A is the change of basis matrix from B₁ to B₂, then A is invertible, and is the change of basis matrix from B₂ to B₁.

Quizplus · Accepted Answer

Since the two bases B₁ and B₂ are for the same subspace, the change of basis matrix A exists and is invertible. The inverse of A is the change of basis matrix from B₂ to B₁, denoted by 11edaba5_20ac_eaa3_a975_794485161261_TBMC1039_00. This implies that both matrices exist and are invertible. Therefore, the answer is A.

If B1, B2 Are Bases for a Given Subspace, and a Is

If B₁, B₂ Are Bases for a Given Subspace, and a Is