MAT223H1 Chapter 5.3: Chapter 5.3 Applications of the Determinant
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Let s be the unit square in the rst quadrant of r2, and consider a linear transformation t : r2 r2. Assume that such linear transformations is represented by the matrix a =(cid:2) a1 a2 (cid:3), so that t (x) = ax. If p = t (s) is the image of s under t , and a is invertible, then p is a parallelogram in r2. A =(cid:2) a1 ai an and b rn. Then, let ai denote the matrix a after replac- ing ai with b. A =(cid:2) a1 (cid:3) ai 1 b ai+1 an. Let a be an invertible n n matrix. Then the components of the unique solution x to ax = b are given by xi = det ai det a (1) for i = 1, 2, . Let a be an n n matrix, and de ne the cofactor matrix by.
