Explain how to compute the determinant of a matrix A by using its LU decomposition. It...

 

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Explain how to compute the determinant of a matrix A by using its LU decomposition. It takes about 2m/3 floating-point operations to compute the LU decomposition of a square matrix of dimension m. Suppose its determinant could be computed with m more multiplications. How long (in milliseconds) would it take a computer that can perform 1 billion (= 10) multiplications per second to compute the determinant of a measly 20 20 matrix using this method? The way most people first learn to compute the determinant of a matrix is by expansion in minors. It can be shown that the number of multiplications required to evaluate the determinant of an m x m matrix in this way is m!(m - 1). How long (in years) would it take a computer that can perform 1 billion (= 10) multiplications per second to compute the determinant of that same measly 20 20 matrix using this method? Explain how to compute the determinant of a matrix A by using its LU decomposition. It takes about 2m/3 floating-point operations to compute the LU decomposition of a square matrix of dimension m. Suppose its determinant could be computed with m more multiplications. How long (in milliseconds) would it take a computer that can perform 1 billion (= 10) multiplications per second to compute the determinant of a measly 20 20 matrix using this method? The way most people first learn to compute the determinant of a matrix is by expansion in minors. It can be shown that the number of multiplications required to evaluate the determinant of an m x m matrix in this way is m!(m - 1). How long (in years) would it take a computer that can perform 1 billion (= 10) multiplications per second to compute the determinant of that same measly 20 20 matrix using this method?