ɪnstˈɛd, ðə dɪtˈɜːmɪnənt kæn biː ɪvˈæljuːˌeɪɾᵻd ɪn ˌɑːpɚɹˈeɪʃənz baɪ fˈɔːɹmɪŋ ðɪ ˌɛljˈuː dˌiːkɑːmpəzˈɪʃən tˈɪpɪkli vˈaɪə ɡˈaʊʃən ᵻlˌɪmᵻnˈeɪʃən ɔːɹ sˈɪmɪlɚ mˈɛθədz, ɪnwˌɪtʃ kˈeɪs ænd ðə dɪtˈɜːmɪnənts ʌvðə tɹaɪˈæŋɡjʊlɚ mˈeɪtɹɪsˌiːz ænd ɑːɹ sˈɪmpli ðə pɹˈɑːdʌkts ʌv ðɛɹ daɪˈæɡənəl ˈɛntɹiz.
Instead, the determinant can be evaluated in  operations by forming the LU decomposition  (typically via Gaussian elimination or similar methods), in which case  and the determinants of the triangular matrices  and  are simply the products of their diagonal entries.