2. [20 marks] Explain how to compute the determinant of a matrix A by using its LU decomposition. It takes about 2m3/3 floating-point operations to compute the LU decomposition of a square matrix of dimension m. Suppose its determinant could be computed with nm more multiplications How long (in milliseconds) would it take a computer that can perform 1 billion109) 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 m matrix in this way is m(m-1) How long (in years) would it take a computer that can perform bi109) multiplications per second to compute the determinant of that same measly 20 x 20 matrix using this method