UnkleRhaukus
  • UnkleRhaukus
\[\newcommand\ve[1]{\vec{\boldsymbol #1}} % vector \newcommand\uv[1]{\hat{\boldsymbol #1}} % unit vector \begin{equation*}\ve A=\begin{bmatrix}a_1\\a_2\\a_3\end{bmatrix}=\langle a_1,a_2,a_3\rangle\\ \end{equation*}\]?
Linear Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
If the column matrix is the same as the vector?
UnkleRhaukus
  • UnkleRhaukus
maybe
UnkleRhaukus
  • UnkleRhaukus
i hope so

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More answers

anonymous
  • anonymous
I don't understand the question (if this is a question) :(
UnkleRhaukus
  • UnkleRhaukus
well i'm trying to understand the different notations,,
klimenkov
  • klimenkov
It depends on the situation. In one case you can use different notations for the vector and in another - you cant.
UnkleRhaukus
  • UnkleRhaukus
can you explain why that is so ?
klimenkov
  • klimenkov
Yes, I can. Do you know anything about matrix multiplication?
UnkleRhaukus
  • UnkleRhaukus
yeah,
klimenkov
  • klimenkov
So I show a case, when the row notation and the column notation should not be confused. Lets take two vectors: \(\vec{a}=\left(\begin{matrix}1\\2\end{matrix}\right)\) and \(\vec{b}=(3,4)\). And now multiply \(\vec{a}\) on \(\vec{b}\), and then \(\vec{b}\) on \(\vec{a}\): \(\vec{a}\vec{b}=\left(\begin{matrix}1\\2\end{matrix}\right)(3,4)=\left(\begin{matrix}3&4\\6&8\end{matrix}\right)\) \(\vec{b}\vec{a}=(3,4)\left(\begin{matrix}1\\2\end{matrix}\right)=3\cdot1+4\cdot2=11\) If we confuse the rows and the columns we will have the wrong result, because it is important to know where is the column and where is the row. But in other case, when we say about a vector in general, without multiplication, it is not so important to know if it is a row or a column.
UnkleRhaukus
  • UnkleRhaukus
do the different vectors fit the same cartesian plane?
klimenkov
  • klimenkov
2D vectors can represent the points of the cartesian plane. So the different vectors represent different points. And they fit this plane.
klimenkov
  • klimenkov
Do you have a concrete example, so I can help you?
UnkleRhaukus
  • UnkleRhaukus
1 Attachment
UnkleRhaukus
  • UnkleRhaukus
or should one of those be on the z axis?
klimenkov
  • klimenkov
It is ok. Why do you think any of those must be on z-axis? One more question: how did you draw this pic?
klimenkov
  • klimenkov
Oh. I thought about it, but it is too long to draw pics in TikZ. Or you have good skills?
UnkleRhaukus
  • UnkleRhaukus
i just made my first 3d template on ti\(k\)z today
UnkleRhaukus
  • UnkleRhaukus
i suppose i think the different vectors look different, so they must be orthogonal somehow
UnkleRhaukus
  • UnkleRhaukus
* i mean the notation is different
klimenkov
  • klimenkov
No. Different vectors on the plane are the vectors, that has different components. The notation doesn't play any role.
UnkleRhaukus
  • UnkleRhaukus
ok so then, the operation of multiplying the vectors somehow chooses that the first vector to be a row vector for dot product, right?
klimenkov
  • klimenkov
Scalar product of the vectors is just a particular case of the general multplication of the matrices.
UnkleRhaukus
  • UnkleRhaukus
can you graph a matrix?
klimenkov
  • klimenkov
You have to know what a matrix interprete. It is a table of numbers. My answer is No.
UnkleRhaukus
  • UnkleRhaukus
not even a 2x2 matrix?
klimenkov
  • klimenkov
No. How do you think, what does this matrix will show on the plane? A components of the vectors can be read as the point, but what is a matrix?
anonymous
  • anonymous
since you written an arrow on top of the A, I assume it is a vector. So the vector is 3 dimensional in R^3. Let the a's equal x, y, and z standing for its components. The second is written in column form and the last one is written in row form. I hope this answers your question. They are both equal but written differently notation wise.

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