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📖 Understanding Linear Algebra
A matrix is a rectangular array of numbers arranged in rows and columns. A matrix with m rows and n columns is called an m×n matrix.
Matrix Addition: Matrices of the same size are added element by element. Matrix Multiplication: (AB)ᵢⱼ = sum of row i of A × column j of B. Note: AB ≠ BA in general.
The determinant of a 2×2 matrix [a b; c d] is det(A) = ad − bc. If det(A) = 0, the matrix is singular (no inverse).
The inverse matrix A⁻¹ satisfies AA⁻¹ = I (identity matrix). For 2×2: A⁻¹ = (1/det(A))[d −b; −c a]. Used to solve systems AX = B → X = A⁻¹B.
🔑 Key Points to Remember
- ✓Matrix: m×n array of numbers
- ✓Matrix multiplication: rows × columns
- ✓det(A) = ad − bc for 2×2
- ✓A⁻¹ exists only when det(A) ≠ 0
- ✓AX = B → X = A⁻¹B
#matrices#linear algebra#determinant#inverse#university
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