Chapter 2.4 Determinants-Applications

The unique solution of ax b is x a1 b we use the

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Unformatted text preview: tion of Ax = b is x = A−1 b. We use the formula for the inverse to compute: x = A−1 b = 1 1 adj(A)b = det A det A n k =1 bk Ck 1 Ck 2 . . . Ckn n k =1 bk Ckj . det A On the other hand, expanding the determinant of Ab,j along the j th column yields the same formula. Hence, xj = Outline The Classical Adjoint A Formula for the Inverse of a Matrix Example Example Use Cramer’s Rule to solve the system A= 2x1 + 3x2 = 7 4x1 + 5x2 = 13 Cramer’s Rule Eigenvalues Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues Eigenvalues of a Matrix Linear systems of equations of the form Ax = λx, for an n × n matrix A and a scalar λ, occur frequently in applications of linear algebra. It is equivalent to the h...
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