What are the values of $k$ that males $x_1,x_2$ solutions to the linear system $AX=B$.

Question

Supose that $x_1$ and $x_2$ are solution to the linear system $ AX=B $ , where $B$ is not equal zero then $3x_1-kx_2$ is a solution also if $k = ?$

How to find the value of $A$ ?

Answer 1

Hints: The fact that $x_1$ and $x_2$ are solutions to $AX = B$ means that $Ax_1 = B$ and $Ax_2 = B$.

In order for $3x_1-kx_2$ to be a solution to $AX=B$, we would need $A(3x_1-kx_2) = B$.

We can use linearity to simplify $A(3x_1-kx_2) = 3Ax_1-kAx_2 = \cdots$.

Can you figure out what value of $k$ makes $A(3x_1-kx_2) = B$?