# Matrix Addition: OK - No Examples Found

• MHB
• karush
In summary, the conversation discusses a problem involving vector spaces and the conditions that must be met. The problem asks if a given set of numbers can satisfy the conditions and the solution is shown using equations.
karush
Gold Member
MHB
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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

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karush said:
I did not see any example of this
Which textbook are you using? Are you sure it does not contain solved similar examples?

karush said:
the circle red is mine ... why is this here
By definition. The author (or anybody) has the right to define whatever concepts they like.

karush said:
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?

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 $$x_1= -1$$?

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## FAQ: Matrix Addition: OK - No Examples Found

Matrix addition is a mathematical operation where two matrices of the same size are added together by adding the corresponding elements in each matrix.

## What are the rules for matrix addition?

The two matrices being added must have the same number of rows and columns. To add them, simply add the corresponding elements in each matrix. For example, if A and B are both 2x2 matrices, then A + B = [a11 + b11, a12 + b12; a21 + b21, a22 + b22].

## Can matrices of different sizes be added together?

No, matrices of different sizes cannot be added together. The number of rows and columns must be the same in order for matrix addition to be possible.

Yes, matrix addition is commutative. This means that the order in which the matrices are added does not affect the result. A + B = B + A.

## What is the purpose of matrix addition?

Matrix addition is used in various fields such as mathematics, physics, and computer science. It is used to simplify and solve complex equations, perform transformations, and manipulate data in matrices.

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