The sum of two lower triangular matrices is always

The sum of two lower triangular matrices is always
  1. an upper triangular matrix
  2. a lower triangular matrix
  3. a diagonal matrix
  4. a scalar matrix

Solution

Let lower triangular matrix $A=\left[\begin{array}{lll}a & 0 & 0 \\ p & b & 0 \\ q & r & c\end{array}\right]$ and $B=\left[\begin{array}{ccc}a_1 & 0 & 0 \\ p_1 & b_1 & 0 \\ q_1 & r_1 & c_1\end{array}\right]$ $A+B=\left[\begin{array}{ccc}a+a_1 & 0 & 0 \\ p+p_1 & b+b_1 & 0 \\ q+q_1 & r+r_1 & c+c_1\end{array}\right]$ Clearly $A+B$ is also lower triangular matrix.

Asked in: AP EAMCET 2021 (24 Aug Shift 2)

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