Final answer:
When we replace R₂ by -6R₁+R₂ in the given matrix, the new matrix is obtained by substituting the values of R₂ with the given expression.
Step-by-step explanation:
When we replace R₂ by -6R₁+R₂, we are substituting the value of -6R₁+R₂ in place of R₂ in the given matrix. The matrix is [rrr 1 & 6 & -3 & -1, 6 & 8 & 8 & 8, -4 & 9 & 6 & -7].
To simplify this, we perform the substitution: -6R₁+R₂ = -6(1) + 6 & -6(6) + 8 & -6(-3) + 8 & -6(-1) + 8. This gives us the new matrix [rrr 0 & 2 & 14 & 2, 6 & 8 & 8 & 8, -4 & 9 & 6 & -7].