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Preparing your Lab
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Matrix Operations
Addition:
[A] + [B] = [a_ij + b_ij]
Scalar Mult:
k[A] = [k·a_ij]
Multiplication:
(AB)_ij = Σ(a_ik · b_kj)
Transpose:
(A^T)_ij = A_ji
Properties
A + B = B + A (Commutative Add)
AB ≠ BA (Non-Commutative Mult)
(AB)^T = B^T A^T
(AB)^-1 = B^-1 A^-1
det(AB) = det(A)det(B)
Determinants & Inverses (2x2)
Determinant
|A| = ad - bc
Inverse
A⁻¹ = (1/|A|) ·
[ d -b ]
[ -c a ]
Cramer's Rule
x = det(Ax) / det(A)
y = det(Ay) / det(A)