Assertion and reason: structure

Exercise and reference answers

Questions

1. Reason

   The chapter states this decomposition explicitly.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Any square matrix splits into a symmetric and a skew symmetric part.

2. Reason

   Addition works entry by entry, so the entries must correspond.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Adding two matrices requires the same order.

3. Reason

   The inverse of a matrix is unique.

   Verdict

   Both are true; the reason does not explain the assertion.

   Assertion

   The transpose swaps rows and columns.

Explanation