Question

Which of the following elementary operations has been applied to the matrix A=\(\begin{bmatrix}8&5\\2&8\end{bmatrix}\) such that the new matrix is \(\begin{bmatrix}12&21\\2&8\end{bmatrix}\)?

(a) R1→R1-2R2

(b) R1→2R1+R2

(c) R1→R2+R1

(d) R1→R1+2R2

The question was posed to me by my school principal while I was bunking the class.

Origin of the question is Elementary Operation (Transformation) of a Matrix in division Matrices of Mathematics – Class 12

Answer 1

Correct option is (d) R1→R1+2R2

To elaborate: The given matrix is A=\(\begin{bmatrix}8&5\\2&8\end{bmatrix}\)

Applying the elementary operation R1→R1+2R2, we get

\(\begin{bmatrix}8+2(2)&5+2(8)\\2&8\end{bmatrix}\)=\(\begin{bmatrix}12&21\\2&8\end{bmatrix}\).