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Precalculus Mathematics Homework Help
Solving these Simultaneous Equations
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[QUOTE="Mark44, post: 6568217, member: 147785"] A somewhat simpler way to solve this system, and possibly the technique the authors of the problem had in mind, is to use the inverse of the given matrix. The inverse of the 2x2 matrix ##A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}## is ##A^{-1} = \frac 1 {det(A)}\begin{bmatrix} d & -b \\ -c & a\end{bmatrix}##. The determinant of A is ##det(A) = ad - bc##. As long as ##ad - bc \ne 0##, the matrix is invertible; i.e., the inverse of A exists. For this problem, ##A = \begin{bmatrix} a + b & -c \\ -a & a + b \end{bmatrix}## To solve the matrix equation ##A\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} bc \\ -ab \end{bmatrix}##, apply the inverse, ##A^{-1}##, to both sides of the matrix equation above to obtain the solution ##\begin{bmatrix} x \\ y \end{bmatrix}##. [/QUOTE]
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Precalculus Mathematics Homework Help
Solving these Simultaneous Equations
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