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Finite Chapter 3.3

Finite Chapter 3.3 - -=-a c b d bc ad d c b a 1 1 …as...

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Math 120 SP08 SBrodnick 1 1 3.3 : Matrix Inversion 2 3.3: Matrix Inversion * Inverse of a Matrix : Inverse of n x n matrix A is n x n matrix A -1 , where A A -1 = A -1 A = I * If A doesn’t have an inverse, it’s singular * Finding Inverse of a Square Matrix : * Put matrix on the left and I on the right * Use row operations to make left side look like I * What’s left on right side is the inverse * If can’t get I on left side, matrix is singular (n x n identity matrix) 3 * In calculator: [A] -1 * Calculator error SingularMat : No Inverse * Another way to find inverse of a 2 x 2
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Unformatted text preview: : ---= -a c b d bc ad d c b a 1 1 …as long as ad – bc ≠ 0 (ad – bc is Determinant of matrix) 3.3: Matrix Inversion 4 * Using Matrix Inversion to Solve a System of Equations : * Write system as a matrix equation * Find inverse of the coefficient matrix A * Multiply both sides of the matrix equation by A-1 (be careful about the order…) * In general, if AX = B, then X = A-1 B Coefficient Matrix Variable Vector Vector of Real Numbers 3.3: Matrix Inversion...
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