Question

Which of the following matrices will remain same if the elementary operation R1→2R1+3R2 is applied on the matrix?

(a) \(\begin{bmatrix}1&2&3\\3&4&1\end{bmatrix}\)

(b) \(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\)

(c) \(\begin{bmatrix}0&1&0\\1&0&1\\0&1&0\end{bmatrix}\)

(d) \(\begin{bmatrix}1&0\\1&2\\1&0\end{bmatrix}\)

This question was posed to me by my school teacher while I was bunking the class.

The above asked question is from Elementary Operation (Transformation) of a Matrix in chapter Matrices of Mathematics – Class 12

Answer 1

Correct choice is (b) \(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\)

To explain: Consider matrix A=\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\), applying the elementary operation R1→2R1+3R2.

\(\begin{bmatrix}2(0)+3(0)&2(0)+3(0)&2(0)+3(0)\\0&0&0\\0&0&0\end{bmatrix}\)=\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\).

Therefore, the matrix A=\(\begin{bmatrix}0&0&0\\0&0&0\\0&0&0\end{bmatrix}\), remains same after applying the elementary operation.