Question

The matrix \[\left[ {\begin{array}{*{20}{c}}
  2&5&{ - 7} \\
  0&3&{11} \\
  0&0&9
\end{array}} \right]\] is known as
A. Symmetric matrix
B. Diagonal matrix
C. Upper triangular matrix
D. Skew symmetric matrix

Answer 1

Hint:In the problem we are given a square matrix of order \[3 \times 3\]. The main diagonal elements are the ones that occur from the top left of the matrix down to the bottom right corner. The main diagonal is also called the major diagonal or the primary diagonal. We observe in the matrix that the elements below the main diagonal elements are zero. Based on this observation we can find the type of the matrix.

Complete step by step Solution:
We are given with a square matrix \[\left[ {\begin{array}{*{20}{c}}
  2&5&{ - 7} \\
  0&3&{11} \\
  0&0&9
\end{array}} \right]\]
We observe that all the elements below the main diagonal in the matrix are zero. The matrix has values only above the main diagonal. So, the given matrix is an upper triangular matrix.

Therefore, the correct option is (C).

Note:To solve the given problem, one must know about the different types of matrices. A square matrix is said to be a triangular matrix if the elements above or below the main diagonal are zero. There are two types of triangular matrices. A square matrix \[\left[ {{a_{ij}}} \right]\]is called an upper triangular matrix, if \[{a_{ij}}\; = {\text{ }}0\], when i > j. A square matrix is called a lower triangular matrix, if \[{a_{ij}}\; = {\text{ }}0\] when i < j.