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What the characteristic equation of egienvalue and egienvector

on 4: find smith canonical form of by elementary row/column operationQuestion5: solve the following system using LU decomposition Next we show how an LU decompostion canbe used to solve asystem of linear equationsStep to solve to a system using an LU decompostion:Set up the equation Find LU decomposition of A this will yield the equation Let .then solve for Take the values of Y and solve for this will gives the solution to the system Question 6: Cholesky DecompositionSuppose A then show the matrix A is SPD and find or Question 6 : for the following matrixFind characteristic equationEigen value and Eigen vectorMinimal polynomialShow cahlyey Hamilton theoremFind inverse of the matrix by cayley Hamilton theorem if exis