Given an example of

Question:

Given an example of

(i) a row matrix which is also a column matrix,

(ii) a diagonal matrix which is not scalar,

(iii) a triangular matrix

Solution:

(i) [6]

This is a matrix that contains only one element.

(ii) $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3\end{array}\right]$

For a diagonal matrix which is not scalar, all elements except those in the leading diagonal should be zero and the elements in the diagonal should not be equal.

(iii) $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 5 & 4 \\ 0 & 0 & 6\end{array}\right]$

Here, all elements below the main diagonal in upper triangular matrix are zero.

$\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 6 & 0 \\ 3 & 4 & 5\end{array}\right]$

Here, all elements above the main diagonal in lower triangular matrix are zero.

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