Find the determinates of the matrix is \( \left[ {\begin{array}{*{20}{c}} 1&221&223\\ 0&4&280\\ 0&0&2 \end{array}} \right]\)  

Concept:

There are two types of matrix Upper and lower triangle  matrix

An example of Upper type matrix  is \( \left[ {\begin{array}{*{20}{c}} a&b&c\\ 0&d&e\\ 0&0&f \end{array}} \right]\)

The determinates of Upper and Lower triangle matrix is the multiplication of main diagonal elements.

The determinates of \( \left[ {\begin{array}{*{20}{c}} a&b&c\\ 0&d&e\\ 0&0&f \end{array}} \right]\) is \(\rm a× d× f\)

Calculation:

Given

\( \left[ {\begin{array}{*{20}{c}} 1&221&223\\ 0&4&280\\ 0&0&2 \end{array}} \right]\)

Determinates of the matrix is \( \left[ {\begin{array}{*{20}{c}} 1&221&223\\ 0&4&280\\ 0&0&2 \end{array}} \right]\)  = 1 × 4 × 2 = 8