Definitions [2]
A matrix is a rectangular arrangement of numbers arranged in rows and columns, enclosed in brackets [ ] or parentheses ( ).
Elements (Entries) of a Matrix
- Each number in a matrix is called an element (or entry).
Rows and Columns
- Horizontal lines → rows
- Vertical lines → columns
Order of a Matrix
- Order = number of rows × number of columns
- Written as m × n and read as “m by n”
A determinant is a single real number associated with a square matrix only.
- Denoted by det A or ∣A∣ or Δ
Formulae [1]
Order 1 (1×1 matrix):
∣A∣ = a
Order 2 (2×2 matrix):
∣A∣ = ad − bc
Order 3 (3×3 matrix):
\[A= \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}\]
\[|A|=a_{11}(a_{22}a_{33}-a_{32}a_{23})-a_{12}(a_{21}a_{33}-a_{31}a_{23})+a_{13}(a_{21}a_{32}-a_{31}a_{22})\]
- If |A| = 0
A matrix is called a Singular Matrix - If |A| ≠ 0
Matrix is called a Non-Singular Matrix
Key Points
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Matrix: A rectangular array of elements.
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Element: An entry inside a matrix.
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Order: Size of a matrix written as rows × columns.
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Row: Horizontal set of elements.
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Column: Vertical set of elements.
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aij: Element in the i-th row and j-th column.
