ALG 10 Matrices et applications linéaires

COFACTOR MATRICES 49 Proof Any matrix B whose (i, j) cofactor is (Y, and whose ith row and jth column are zero, satisfies cof( B) = (Y Eij n For example, let u be the one-to-one mapping of S = (1,

Minors, Cofactors, Cramers Rule and Adjoints

4 o Example: Find IA I = o 10 1 o 3 2 5 Expand along 1st column: IA = c 01 3 Cramer's Rule ( co ex —20 — -38 Consider a system of linear equations represented in matrix form as = b

Lecture 36: Minors and cofactors

De nitions and motivation Lemma 3 10 Let A = [c1;:::;cn] be an n n matrix, and de ne B by adding kc i to the jth column, for i 6= j Then detA = detB De nition Let A be an n n matrix, and let A

Inverse of a Matrix using Minors, Cofactors and Adjugate

(It gets harder for a 3×3 matrix, etc) The Calculations Here are the first two, and last two, calculations of the "Matrix of Minors" (notice how I ignore the values in the current row and columns, and calculate the determinant using the

Lecture 19: Determinant formulas and cofactors

The number of parts with non-zero determinants was 2 in the 2 by 2 case, 6 in the 3 by 3 case, and will be 24 = 4 in the 4 by 4 case This is because

LINEAR ALGEBRA & MATRICES

1 Review of Matrix Algebra 3 A scalar is a 1×1 matrix If m = n the matrix is said to be square If m = 1 the matrix is a row matrix (or vector)