Final answer:
To perform the elementary row operation (1)/(2)R_3 -> R_3 on the given matrix, we multiply the third row by 1/2.
Step-by-step explanation:
To perform the elementary row operation (1)/(2)R_3 -> R_3 on the given matrix, we multiply the third row by 1/2.
The given matrix is [[5,3,1,4],[3,1,3,1],[5,3,-3,10]].
Multiplying the third row by 1/2 results in [[5,3,1,4],[3,1,3,1],[2,3/2,-3/2,5]].
So, the new matrix after performing the elementary row operation is [[5,3,1,4],[3,1,3,1],[2,3/2,-3/2,5]].