Whakaoti i te {ccc}{1}&{1}&{1}{0}&{2}&{3}{5}&{5}&{1}*{rrr}{13/8}&{-1/2}&{-1/8}{-15/8}&{frac{1}{2}}&{frac{3}{8}}{frac{5}{4}}&{0}&{-frac{1}{4}}=

$$\left( \begin{array} { c c c } { 1 } & { 1 } & { 1 } \\ { 0 } & { 2 } & { 3 } \\ { 5 } & { 5 } & { 1 } \end{array} \right) \cdot \left( \begin{array} { r r r } { \frac { 13 } { 8 } } & { - \frac { 1 } { 2 } } & { - \frac { 1 } { 8 } } \\ { - \frac { 15 } { 8 } } & { \frac { 1 } { 2 } } & { \frac { 3 } { 8 } } \\ { \frac { 5 } { 4 } } & { 0 } & { - \frac { 1 } { 4 } } \end{array} \right) =$$

Aromātai

$$\left(\begin{matrix}1&0&0\\0&1&0\\0&0&1\end{matrix}\right)$$

Ngā Upane e Whakamahi ana i te Ture Whakarea Poukapa

Ka tautuhia te whakareanga poukapa mēnā he ōrite te tau o ngā tīwae o te poukapa tuatahi ki te tau o ngā rārangi o te poukapa tuarua.

$$\left(\begin{matrix}1&1&1\\0&2&3\\5&5&1\end{matrix}\right)\left(\begin{matrix}\frac{13}{8}&-\frac{1}{2}&-\frac{1}{8}\\-\frac{15}{8}&\frac{1}{2}&\frac{3}{8}\\\frac{5}{4}&0&-\frac{1}{4}\end{matrix}\right)$$

Whakareatia ia huānga o te rārangi tuatahi o te poukapa tuatahi ki te huānga hāngai o te tīwae tuatahi o te poukapa tuarua kā tāpiri i ēnei hua kia kitea ai te huānga i te rārangi tuatahi, tīwae tuatahi o te poukapa hua.

$$\left(\begin{matrix}\frac{13}{8}-\frac{15}{8}+\frac{5}{4}&&\\&&\\&&\end{matrix}\right)$$

Ka kitea ngā toenga huānga o te poukapa hua mā taua tikanga anō.

$$\left(\begin{matrix}\frac{13}{8}-\frac{15}{8}+\frac{5}{4}&\frac{-1+1}{2}&-\frac{1}{8}+\frac{3}{8}-\frac{1}{4}\\2\left(-\frac{15}{8}\right)+3\times \frac{5}{4}&2\times \frac{1}{2}&2\times \frac{3}{8}+3\left(-\frac{1}{4}\right)\\5\times \frac{13}{8}+5\left(-\frac{15}{8}\right)+\frac{5}{4}&5\left(-\frac{1}{2}\right)+5\times \frac{1}{2}&5\left(-\frac{1}{8}\right)+5\times \frac{3}{8}-\frac{1}{4}\end{matrix}\right)$$

Whakarūnātia ia huānga mā te whakarea i ngā kīanga tau takitahi.

$$\left(\begin{matrix}\frac{13}{8}-\frac{15}{8}+\frac{5}{4}&\frac{-1+1}{2}&-\frac{1}{8}+\frac{3}{8}-\frac{1}{4}\\\frac{-15+15}{4}&1&\frac{3-3}{4}\\\frac{65}{8}-\frac{75}{8}+\frac{5}{4}&\frac{-5+5}{2}&-\frac{5}{8}+\frac{15}{8}-\frac{1}{4}\end{matrix}\right)$$

Tapekehia ia huānga o te poukapa.

$$\left(\begin{matrix}1&0&0\\0&1&0\\0&0&1\end{matrix}\right)$$

Tātai Tau Whakatau

$$1$$