Matrix Operations Flashcards

Grade 11 · Math · Flashcards

Core matrix concepts including dimensions, operations, determinants, and inverses.

Flashcards

Matrix addition: Add corresponding elements; requires same dimensions
Scalar multiplication: Multiply every element by the scalar k
Matrix multiplication condition: A(m×n) * B(n×p) = C(m×p); inner dimensions must match
Matrix multiplication (not commutative): AB ≠ BA in general; order matters
Identity matrix: Square matrix with 1s on diagonal, 0s elsewhere; AI = IA = A
Zero matrix: Matrix of all zeros; A + 0 = A
2×2 determinant: det[[a,b],[c,d]] = ad - bc
Singular matrix: det(A) = 0; no inverse exists; system has no unique solution
2×2 inverse formula: A⁻¹ = (1/det(A)) * [[d,-b],[-c,a]]
Solving AX = B: X = A⁻¹B, provided det(A) ≠ 0
Cramer's Rule: x_i = det(A_i)/det(A); replace ith column of A with constant vector
Transpose matrix: A^T flips rows and columns; (A^T)_ij = A_ji
det(AB) property: det(AB) = det(A) · det(B) for same-sized square matrices