What is the Inverse Matrix for A?

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SUMMARY

The discussion focuses on finding the inverse matrix for a given 2x2 matrix A, defined as A = [ -4e^4t sin(9t) -4e^5t cos(9t); 4e^4t cos(9t) -4te^5t sin(9t) ]. The method proposed involves using the Reduced Row Echelon Form (RREF) to derive the inverse. The key equation utilized is that a matrix multiplied by its inverse results in the identity matrix, leading to a system of equations to solve for the unknown elements of the inverse matrix.

PREREQUISITES
  • Understanding of matrix operations, specifically matrix inversion
  • Familiarity with Reduced Row Echelon Form (RREF)
  • Knowledge of exponential functions and trigonometric identities
  • Basic algebra skills for solving systems of equations
NEXT STEPS
  • Study the process of finding the inverse of a matrix using RREF
  • Learn about the properties of matrix multiplication and the identity matrix
  • Explore the application of exponential and trigonometric functions in matrix equations
  • Practice solving systems of equations derived from matrix operations
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Students in linear algebra, mathematicians, and anyone involved in solving matrix equations or studying matrix theory.

LaraCroft
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Homework Statement



If A =

[ -4e^4t sin(9t) -4e^5t cos (9t) ]
[ 4e^4t cos (9t) -4te^5t sin (9t) ]

then A^-1 =

[ ___ ___ ]
[ ___ ___ ]

Homework Equations



how do you deal with the exponents?

The Attempt at a Solution


Put into RREF, and then see what the inverse is?
 
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Well, you know that a matrix times its inverse gives the identity matrix. Set up the inverse matrix as having four unknown numbers in it (a,b,c,d for instance) and plug it into the equation I just mentioned. This will give you some equations to solve to find the parts of the inverse matrix.
 

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