Given Information
We are given with following matrix: \[A = \left[ \begin{array} { r r r r r } { 8 } & { - 3 } & { 0 } & { - 7 } & { 2 } \\ { - 9 } & { 4 } & { 5 } & { 11 } & { - 7 } \\ { 6 } & { - 2 } & { 2 } & { - 4 } & { 4 } \\ { 5 } & { - 1 } & { 7 } & { 0 } & { 10 } \end{array} \right]\]We have to show that each linearly dependent column in A is in the set spanned by the columns of B.

Step-1:
Find the Row-reduce echelon form using MATLAB

>> A = [3 -4 10 7 -4 ; -5 -3 -7 -11 15; 4 3 5 2 1; 8 -7 23 4 15];
>> U=rref(A)\[U = \left[ {\begin{array}{*{20}{r}}1&0&2&0&2\\0&1&{ - 1}&0&{ - 1}\\0&0&0&1&{ - 2}\\0&0&0&0&0\end{array}} \right]\]Since the columns 1, 2 and 4 have pivot elements, hence these columns are linearly independent and remaining columns are combinations of these three columns.

Step-2: The matrix B and V
Construct the Matrix B by using linearly independent columns. \[B = \left[ \begin{array} { c c c } { 3 } & { - 4 } & { 7 } \\ { - 5 } & { - 3 } & { - 11 } \\ { 4 } & { 3 } & { 2 } \\ { 8 } & { - 7 } & { 4 } \end{array} \right]\]Select one of the dependent vector: \[\mathbf { v } = \left[ \begin{array} { c } { - 4 } \\ { 15 } \\ { 1 } \\ { 15 } \end{array} \right]\]

Step-3: The augmented Matrix
\[[ B \mathbf { v } ] = \left[ \begin{array} { c c c c } { 3 } & { - 4 } & { 7 } & { - 4 } \\ { - 5 } & { - 3 } & { - 11 } & { 15 } \\ { 4 } & { 3 } & { 2 } & { 1 } \\ { 8 } & { - 7 } & { 4 } & { 15 } \end{array} \right]\]

Step-4: Row-reduce the matrix
Using MATLAB:

>> M=[ 3 -4 7 -4; -5 -3 -11 15; 4 3 2 1; 8 -7 4 15];
>> U=rref(M);

\[U = \left[ {\begin{array}{*{20}{r}}1&0&0&2\\0&1&0&{ - 1}\\0&0&1&{ - 2}\\0&0&0&0\end{array}} \right]\]Since, there are three pivot elements, Therefore, Therefore,

Every linearly dependent column in A is in the set spanned by the columns of B.