Inverse Matrix: Real-Life Applications & Uses

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The inverse matrix is primarily used in applications involving multiple linear equations where the coefficient matrix remains constant while the outcome matrix varies. Instead of solving each equation individually, one can compute the inverse of the matrix once and then apply it to different outcome matrices for efficiency. This approach highlights the systemic properties of the matrix A and the specific characteristics of matrix B. Real-life applications include areas such as engineering, computer graphics, and economics, where systems of equations frequently arise. Understanding the inverse matrix can significantly streamline problem-solving in these contexts.
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What use is the inverse matrix?
I would not use it to solve linear systems but there must be some concrete or real life applications where it is used.
 
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There is a sort of "meta" mathematical statement that when you have an application that reduces to an equation like Ax= B, the matrix "A" involves "systemic" properties while the matrix "B" involves properties specific to the problem. It is not unusual to have an application in which you must solve many equations, Ax= B, in which A remains the same while B changes. In that case, it is most efficient to solve for the inverse of A once, then multiply that inverse by the various B matrices.
 
Thanks for the quick response and good answer.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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