Define a symmetric matrix. Give one example of order $3 imes 3$.

Question

Define a symmetric matrix. Give one example of order $3 	imes 3$.

Accepted Answer

>

> [!TLDR]
> A symmetric matrix satisfies $A'=A$; the entries are mirror images across the main diagonal.
>
> A square matrix $A = [a_{ij}]$ is called a **symmetric matrix** if its transpose equals itself, that is
> $$A' = A \quad \Longleftrightarrow \quad a_{ij} = a_{ji} 	ext{ for all } i, j.$$
> Geometrically, the entry in row $i$, column $j$ equals the entry in row $j$, column $i$, so the matrix is unchanged when reflected in the main diagonal.
>
> Example of order $3 	imes 3$: …

Operation	What it asks	Bucket contains
Union ( $A \cup B$ )	In either?	Everything from $A$ or $B$ (or both)
Intersection ( $A \cap B$ )	In both?	Only the overlap
Difference ( $A \setminus B$ )	In $A$ but not $B$ ?	Just the part of $A$ that doesn't touch $B$
Complement ( $A^c$ )	Not in $A$ ?	Everything outside $A$ (inside $U$ )
Symmetric Difference ( $A \triangle B$ )	In exactly one?	The two crescent-shaped parts, excluding the overlap

Q.Define a symmetric matrix. Give one example of order $3 \times 3$ .

Concept understanding — Set Operations

The idea in plain words

Why this works

Step by step

A common slip …

Q.Define a symmetric matrix. Give one example of order 3×33 \times 33×3.

🎓Unlock everything free for 14 days

Q.Define a symmetric matrix. Give one example of order $3 \times 3$ .

Unlock everything free for 14 days