How to turn one column of the matrix into all zeros?

Question

I have a matrix like this:

I search for mathmatical operation that would turn a given column (say $T_3$ or $T_4$) into all zeros not changing anything else about this matrix. How to do such thing in math?

Answer 1

Recall that in general for $A_{m\times n}B_{n\times n}=C_{m\times n}$ the i-th column of $C$ is the combination of the columns of $A$ with respect to the coefficient of the i-th column of $B$.

Then we can multiply by the matrix

\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&0\end{bmatrix}

to obtain a matrix with $T_4=0$ and similarly we can obtain a matrix with $T_3=0$.