These linear systems are all what researchers call one-dimensional.

这些线性系统都是研究人员所说的一维系统。

And that system basically is so for every new number you add a new finger, what researchers call a linear system.

这个系统大致是这样的，每增加一个新数字，你就增加一根新手指，研究人员称之为线性系统。

A linear system would not be able to discover cracks forming around the rivet holes, because a hole would create one big echo.

线性系统不能发现铆钉孔周围的裂纹，因为这种孔能制造出巨大的回音。

It's in part because they sort of break this nice linear system.

部分原因是它们打破了这个良好的线性系统。

Solving a linear system with an orthonormal matrix is actually super easy, because dot products are preserved.

用标准正交矩阵求解线性方程组其实非常简单 因为点积被保留了。

I bringing this up when this idea breaks down for almost all linear systems?

当这个观点在几乎所有线性系统中都不成立的时候？

That's the whole point of a linear system of equations.

这就是线性方程组的意义所在。

This is called a linear system of equations.

这被称为线性方程组。

The relevant background here is understanding determinance, little bit of dot products, and of course, linear systems of equations.

相关的背景知识是理解行列式 一点点积 当然还有线性方程组。

So the set appear will be some linear system of equations, say, with two unknowns, X and Y, and two equations.

所以集合是一个线性方程组 有两个未知数 X和Y 有两个方程。

So that's a very high level overview of how to think about linear systems of equations.

这就是如何思考线性方程组的一个非常高水平的概述。

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。

But 1st, I should say up front that this creamer's rule is not actually the best way for computing solutions to linear systems of equations.

但首先 我要提前说一下 这个奶油法则实际上并不是计算线性方程组解的最佳方法。

What we have is a known transformation given by some three by three matrix and a known output factor given by the right side of our linear system.

我们有一个已知的由某个3×3矩阵给出的变换和一个已知的由线性系统右边给出的输出因子。

It's the space of all vectors that become no in the sense that they land on the zero in terms of the linear system of equations.

它是所有向量组成的空间它们在线性方程组中落在0点上。

Wrapping your mind around this concept is going to help consolidate ideas from linear algebra, like the determinant and linear systems, by seeing how they relate to each other.

把你的思维围绕在这个概念上有助于巩固线性代数的概念 比如行列式和线性系统 通过观察它们之间的关系。

Next up, I'll be relating the idea of linear transformations covered so far to one of the areas where linear algebra is most useful linear systems of equations.

接下来 我将把迄今为止所涉及的线性变换的思想与线性代数最有用的线性方程组的一个领域联系起来。

Most important here is that you know how to think about matrices as linear transformations, but you also need to be comfortable with things like determinants, linear systems of equations and change of basis.

这里最重要的是你知道如何把矩阵看作线性变换 但你也需要熟悉行列式 线性方程组和基底变换。