So again, just using data from the output space, the numbers we see in our original linear system, we can solve for what X must be.

再一次 只要使用输出空间的数据 我们在原始线性系统中看到的数字 我们就能解出X的值。

So that means we can solve for why by taking the area of this new parallelogram in the output space divided by the determinant of the full transformation.

这意味着我们可以通过用输出空间中这个新的平行四边形的面积除以完整变换的行列式来解决问题。

The lesson here is that any time you have one of these linear transformations whose output space is the number line, no matter how it was defined, there's going to be some unique vector V corresponding to that transformation.

这里的经验是 任何时候你有一个这样的线性变换它的输出空间是数轴 不管它是怎么定义的 都会有某个唯一的向量V对应于这个变换。