Ch 3 introduces matrices — rectangular arrays of numbers. Students learn types, operations (addition, scalar multiplication, matrix multiplication), transpose, and properties of symmetric/skew-symmetric matrices.
Row matrix (1 row), column matrix (1 column), square matrix, diagonal matrix, scalar matrix, identity matrix (I), zero matrix. Symmetric: A = Aᵀ. Skew-symmetric: A = −Aᵀ.
Addition: only for matrices of same order, element-wise. Multiplication: A(m×n) × B(n×p) = C(m×p). AB ≠ BA in general (not commutative). AI = IA = A. Matrix multiplication is associative.
(Aᵀ)ᵀ = A. (A+B)ᵀ = Aᵀ+Bᵀ. (kA)ᵀ = kAᵀ. (AB)ᵀ = BᵀAᵀ. Any square matrix can be written as sum of symmetric and skew-symmetric matrices: A = ½(A+Aᵀ) + ½(A−Aᵀ).
Download: https://ncert.nic.in/textbook/pdf/lemh103.pdf | Complete book Part I: https://ncert.nic.in/textbook/pdf/lemh1ps.zip
AB and BA may not even be defined (different dimensions). Even for square matrices, matrix multiplication represents composition of linear transformations, and the order of transformations matters — rotating then scaling is different from scaling then rotating.
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