Are the columns of the following matrix linearly independent? \[ A=\left(\begin{array}{llll} 1 & 1 & 1 & 6 \\ 1 & 2 & 3 & 4 \\ 1 & 3 & 5 & 2 \\ 1 & 4 & 7 & 0 \end{array}\right) \] Yes D. $\mathrm{No}$

Step 1 ：We are given the matrix \(A=\left(\begin{array}{llll} 1 & 1 & 1 & 6 \ 1 & 2 & 3 & 4 \ 1 & 3 & 5 & 2 \ 1 & 4 & 7 & 0 \end{array}\right)\) and asked to determine if its columns are linearly independent.

Step 2 ：To determine if the columns of a matrix are linearly independent, we can perform Gaussian elimination or calculate the determinant of the matrix.

Step 3 ：If the determinant is non-zero, the columns are linearly independent. If the determinant is zero, the columns are linearly dependent.

Step 4 ：Let's calculate the determinant of the matrix.

Step 5 ：The determinant of the matrix is approximately zero.

Step 6 ：This indicates that the columns of the matrix are linearly dependent, not linearly independent.

Step 7 ：\(\boxed{\text{No, the columns of the matrix are not linearly independent.}}\)