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NDA Math Matrices

Question : 56 of 69

Marks: +1, -0

Solution:

An elementary matrix is a square matrix which differs from the identity matrix of the same order by one single elementary row operation.

Consider the matrix given in Option B.

M=\begin{pmatrix}1&5&0\\0&1&0\\0&0&1\end{pmatrix}

R_1 \leftrightarrow R_1 - 5R_2

makes it

\begin{pmatrix}1&5-(5\times1)&0\\0&1&0\\0&0&1\end{pmatrix} = \begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}

which is an Identity matrix.

Thus the matrix M differs from the identity matrix (order 3) by one single row operation.

Hence matrix M is an elementary matrix.

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