Linear Algebra : The Transpose

Study concepts, example questions & explanations for Linear Algebra

varsity tutors app store varsity tutors android store

Example Questions

Example Question #41 : The Transpose

True or false; The set of all  symmetric matrices is a subspace of all matrices. 

Possible Answers:

True

False

Correct answer:

True

Explanation:

Without being too abstract, it is easy to convince oneself that this is true. We have to check the 3 criteria for a subspace.

1. Closure under vector addition

Adding together two symmetric matrices will always result in another symmetric matrix.

2. Closure under scalar multiplication.

Multiplying a symmetric matrix by a scalar will also always give you another symmetric matrix

3. The zero vector (matrix in this case) is also in the subset

Indeed the zero vector itself is a symmetric matrix.

Learning Tools by Varsity Tutors