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
det A n
k =1 bk Ck 1
k =1 bk Ckj .
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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