Q98 / 150 · MHT CET 2026 (13 April Shift 1) · Mathematics
Let $A = \begin{bmatrix} -5 & -3 \\ 2 & 1 \end{bmatrix}$. The Row transformation $R_1 \rightarrow R_1 + 3R_2$ will transform matrix A into
- Aan upper triangular matrix
- Correct answerBa lower triangular matrix
- Can identity matrix
- Da singular matrix
Solution
Given $A = \begin{bmatrix} -5 & -3 \\ 2 & 1 \end{bmatrix}$
Applying the row transformation $R_1 \rightarrow R_1 + 3R_2$, the elements of the first row become:
$a_{11} = -5 + 3(2) = 1$
$a_{12} = -3 + 3(1) = 0$
The transformed matrix is $\begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}$.
Since all elements above the principal diagonal are zero, it is a lower triangular matrix.
Answer: a lower triangular matrix
Applying the row transformation $R_1 \rightarrow R_1 + 3R_2$, the elements of the first row become:
$a_{11} = -5 + 3(2) = 1$
$a_{12} = -3 + 3(1) = 0$
The transformed matrix is $\begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}$.
Since all elements above the principal diagonal are zero, it is a lower triangular matrix.
Answer: a lower triangular matrix
Hence, the correct answer is option: 'B'.