You drive from your house to the dry cleaners, which is 12 miles east of your house. You then drive to the grocery store from the dry cleaners. The grocery store is 15 miles west of your house. You then drive back home from the grocery store. What was your displacement?

15 miles.

Explanation:

Displacement is the position you are in now relative to the position you were in when you started. If you had stopped at the dry cleaner's, your displacement would be 12 miles. However, you traveled back to your house and then 15 miles West of that, meaning you are now 15 miles away from your starting position.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.