Question

For the matrices \[P=\frac{1}{2}(B+B^T)\] and \[Q=\frac{1}{2}(B-B^T)\], what is \[P+Q\]?

Options

• \[B+B^T\]

• \[B\]

• \[0\]

• \[B^T\]

Answer 1

Adding \[P\] and \[Q\] gives \[\frac{1}{2}(B+B^T)+\frac{1}{2}(B-B^T)\]. The \[B^T\] terms cancel, leaving \[B\].