Final answer:
To perform the row operation 4R₂ → R₂ on the given matrix, each element in the second row is multiplied by 4 to yield a new second row of [24, -36, -12, 24]. The transformed matrix then has this new second row while the other rows remain unchanged.
Step-by-step explanation:
The question involves performing a row operation on a matrix, which is a common mathematical operation in linear algebra, a subject typically taught in high school or college. Here, we're asked to multiply the second row (R₂) of the matrix by 4. The given matrix is:
[[2, 5, 2, -6],
[6, -9, -3, 6],
[2, -8, -6, 3]]
To perform the 4R₂ → R₂ operation, we multiply each element of the second row by 4:
[6*4, -9*4, -3*4, 6*4]
This results in the new second row:
[24, -36, -12, 24]
So, our new matrix after the row operation will be:
[[2, 5, 2, -6],
[24, -36, -12, 24],
[2, -8, -6, 3]]
The row operation has been successfully applied to transform the matrix.