Topic explanation

Standard explanation

[[1,2,3],[4,5,6]]^T is 3x2 with columns (1,4), (2,5), (3,6). A square matrix may equal its transpose (symmetric) - named idea if asked.

Key points

• m x n becomes n x m
• rows <-> columns
• (AB)^T = B^T A^T
• keep the ideas separate
• Transpose: [[1,2,3],[4,5,6]]^T is 3x2 with columns (1,4), (2,5), (3,6). A square matrix may equal its transpose
• WHAT — TRANSPOSE: [[1,2,3],[4,5,6]]^T is 3x2 with columns (1,4), (2,5), (3,6). A square matrix may equal its transpose
• HOW — Use the idea: Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check
• CORE UNDERSTANDING: [[1,2,3],[4,5,6]]^T is 3x2 with columns (1,4), (2,5), (3,6). A square matrix may equal its transpose

Labelled diagram