Question

The new matrix after applying the elementary operation R2→2R2+3R1 on the matrix A=\(\begin{bmatrix}2&5&4\\5&2&6\\7&2&1\end{bmatrix}\) is _____________

(a) \(\begin{bmatrix}2&5&4\\16&19&24\\7&2&1\end{bmatrix}\)

(b) \(\begin{bmatrix}2&5&4\\19&19&24\\7&2&1\end{bmatrix}\)

(c) \(\begin{bmatrix}2&-5&4\\16&19&24\\7&2&1\end{bmatrix}\)

(d) \(\begin{bmatrix}1&5&4\\16&19&24\\7&2&1\end{bmatrix}\)

The question was asked in semester exam.

Question is from Elementary Operation (Transformation) of a Matrix topic in division Matrices of Mathematics – Class 12

Answer 1

Right option is (a) \(\begin{bmatrix}2&5&4\\16&19&24\\7&2&1\end{bmatrix}\)

The best explanation: Consider A=\(\begin{bmatrix}2&5&4\\5&2&6\\7&2&1\end{bmatrix}\), after applying R2→2R2+3R1

⇒\(\begin{bmatrix}2&5&4\\2(5)+3(2)&2(2)+3(5)&2(6)+3(4)\\7&2&1\end{bmatrix}\)=\(\begin{bmatrix}2&5&4\\16&19&24\\7&2&1\end{bmatrix}\).