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In Row Vectors Matrix we have system of linear equations and x,y,z are axes in vector space. $$a_1x + b_1y + c_1z = d$$ $$a_2x + b_2y + c_2z= e$$ $$a_3x + b_3y + c_3z = f$$ $$\begin{bmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{bmatrix} \begin{bmatrix}x\\y\\z\end{bmatrix} = \begin{bmatrix}d\\e\\f\end{bmatrix}$$ How & Why we treat above matrix for column operation because this has row vectors?

Also in Column Matrix what is the pattern of system of linear equations?

$$\begin{bmatrix}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{bmatrix}\begin{bmatrix}?\\?\\?\end{bmatrix} = \begin{bmatrix}?\\?\\?\end{bmatrix}$$ What is the correct way of writing in matrix form also how to write system of linear equation for which can be use for column operation?

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Using columns the system becomes

$$xC_1+yC_2+zC_3=D$$ where $C_i$ stands for the $i^{th}$ column.

That is $$x\begin{bmatrix}a_1\\a_2\\a_3\end{bmatrix} + y\begin{bmatrix}b_1\\b_2\\b_3\end{bmatrix}+ z\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix}= \begin{bmatrix}d\\e\\f\end{bmatrix}$$

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  • $\begingroup$ Thanks for the reply. Do you pls explain by writing complete matrix and linear equations? $\endgroup$ – 123 Oct 13 '19 at 20:47
  • $\begingroup$ Why we use row vectors for column operation? Is it allowed how? $\endgroup$ – 123 Oct 13 '19 at 20:56
  • $\begingroup$ @123 It is the same system just different way of writing $\endgroup$ – Mohammad Riazi-Kermani Oct 13 '19 at 21:08
  • $\begingroup$ Thanks, but how can we treat row vector for column operations? how can x component of vectors can be add subtract with y & z components. $\endgroup$ – 123 Oct 13 '19 at 21:13

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