Let A = begin{bmatrix} -5 & -3 2 & 1 end{bma | vedclass

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(B) Given $A = \begin{bmatrix} -5 & -3 \ 2 & 1 \end{bmatrix}$.Applying the row transformation $R_1 	o R_1 + 3R_2$:New $R_1 = [-5 + 3(2), -3 + 3(1)]

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a lower triangular matrix

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(B) Given $A = \begin{bmatrix} -5 & -3 \ 2 & 1 \end{bmatrix}$.Applying the row transformation $R_1 	o R_1 + 3R_2$:New $R_1 = [-5 + 3(2), -3 + 3(1)] = [-5 + 6, -3 + 3] = [1, 0]$.The transformed matrix is $A' = \begin{bmatrix} 1 & 0 \ 2 & 1 \end{bmatrix}$.In an upper triangular matrix, all elements below the main diagonal are zero. Here, the element at position $(2, 1)$ is $2$, so it is not upper triangular.In a lower triangular matrix, all elements above the main diagonal are zero. Here, the element at position $(1, 2)$ is $0$. Since the element above the main diagonal is zero, it is a lower triangular matrix.

Let $A = \begin{bmatrix} -5 & -3 \\ 2 & 1 \end{bmatrix}$. The row transformation $R_1 \to R_1 + 3R_2$ will transform matrix $A$ into

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