Matrix V12=mV: m1v1+m2v2=m12v12 eqn1, m12=m1+m2 eqn2

[ekojerry]

I need help with the below as am totally lost

m1v1+m2v2=m12v12 eqn1
m12=m1+m2 eqn2

rewrite equation 1 after substituting eqn2 so that it in a matrix form.
There should be unknown vector v12 which is equal to a matrix containing all mass term multiple by a velocity vector.

v1= 0.8
v2= 9.5
m1= 5.4
m2= 3.3

 

[tkhunny]

Looks like we might need a little better description of what it is you are doing.

What's stopping you from substituting? Eqn 2 is already solved for m12.

 

[ekojerry]

Looks like we might need a little better description of what it is you are doing.

What's stopping you from substituting? Eqn 2 is already solved for m12.

They just want the equation to be represnted in matrix form after replacing m12 = m1+m2 from equation 2. Which is straight but am cofuse on how to represent it in matrix form

 

[HallsofIvy]

\(\displaystyle m_1v_1+ m_2v_2= m_{12}v_{12}= (m_1+ m_2)v_{12}\)

If you really must write it in "matrix" form, then
\(\displaystyle \begin{bmatrix}m_1 &m_2\end{bmatrix}\begin{bmatrix}v_2 \\ v_2\end{bmatrix}= (m_1+ m_2)v_{12}\).

 

[ekojerry]

\(\displaystyle m_1v_1+ m_2v_2= m_{12}v_{12}= (m_1+ m_2)v_{12}\)

If you really must write it in "matrix" form, then
\(\displaystyle \begin{bmatrix}m_1 &m_2\end{bmatrix}\begin{bmatrix}v_2 \\ v_2\end{bmatrix}= (m_1+ m_2)v_{12}\).

Thanks very much. This is what i know, but just getting myself confuse with making v12 the subject of the formular before converting to matrix

 

[Deleted member 4993]

\(\displaystyle m_1v_1+ m_2v_2= m_{12}v_{12}= (m_1+ m_2)v_{12}\)

If you really must write it in "matrix" form, then
\(\displaystyle \begin{bmatrix}m_1 &m_2\end{bmatrix}\begin{bmatrix}v_2 \\ v_2\end{bmatrix}= (m_1+ m_2)v_{12}\).

Or equivqlently:

\(\displaystyle \begin{bmatrix}m_1 &m_2\end{bmatrix}\begin{bmatrix}v_2 \\ v_2\end{bmatrix}= v_{12} \ * \left(\begin{bmatrix}m_1 &m_2\end{bmatrix}\begin{bmatrix}1 \\ 1\end{bmatrix}\right)\)