Matrix Addition: OK - No Examples Found

[karush]

View attachment 8764

OK from the text bk I did not see any example of this
the circle red is mine ... why is this here

so not sure how these questions are to be answered.

Much Mahalo

 

[Evgeny.Makarov]

I did not see any example of this

Which textbook are you using? Are you sure it does not contain solved similar examples?

the circle red is mine ... why is this here

By definition. The author (or anybody) has the right to define whatever concepts they like.

so not sure how these questions are to be answered.

The problem asks whether this is a vector space. Do you know the definition of a vector space?

 

[HOI]

One condition is that a vector space have a 0 vector. That means that there exist a vector 0 such that v+ 0= v for every vector v. Here it is clear that $$\begin{bmatrix}0 \\ 0 \end{bmatrix}$$ is that 0 vector.

Another condition is that every vector has a "negative". That is, given a vector v, there exist a vector u such that u+ v= v+ u= 0.

Here that means that, given $$v= \begin{bmatrix}x_1 \\ x_2 \end{bmatrix}$$, there exist a vector $$u= \begin{bmatrix}x_2 \\ y_2 \end{bmatrix}$$ such that $$u+ v= \begin{bmatrix}x_1+ x_2+ x_1x_2 \\ y_1+ y_2+ y_1y_2\end{bmatrix}= \begin{bmatrix}0 \\ 0 \end{bmatrix}$$

So the question is, given numbers $$x_1$$, $$y_2$$, can we solve the equations $$x_1+ x_2+ x_1x_2= 0$$ and $$y_1+ y_2+ y_1y_2= 0$$ for $$x_1$$ and $$x_2$$? We can write the first equation $$x_1= -(x_2+ x_1_2)= -x_2(1+ x_1)$$ and then $$x_2= -\frac{x_1}{1+ x_1}$$. What if $$x_1= -1$$?