@shamil98 Seen the matrix method for that?

Question

shamil98 · Answer

I haven't actually.

e.mccormick · Answer

L = S + M - 4
L + S + M = 70
2S = L-9

L - S - M = - 4
L + S + M = 70
-L + 2S+0M =-9

$\left[\begin{array}{ccc|c}
1 & -1 & -1 & -4\
1 & 1 & 1 & 70\
-1 & 2 & 0 & -9
\end{array}\right]$

Add R1 and R2 new R1

$\left[\begin{array}{ccc|c}
2 & 0 & 0 & 66\
1 & 1 & 1 & 70\
-1 & 2 & 0 & -9
\end{array}\right]$

R1 $\times \dfrac{1}{2}$

$\left[\begin{array}{ccc|c}
1 & 0 & 0 & 33\
1 & 1 & 1 & 70\
-1 & 2 & 0 & -9
\end{array}\right]$

R2 + (-1)R1 new R2
R3 + R1 new R1

$\left[\begin{array}{ccc|c}
1 & 0 & 0 & 33\
0 & 1 & 1 & 37\
0 & 2 & 0 & 24
\end{array}\right]$

$R3 \(\times \dfrac{1}{2}$

$\left[\begin{array}{ccc|c}
1 & 0 & 0 & 33\
0 & 1 & 1 & 37\
0 & 1 & 0 & 12
\end{array}\right]$
R2 + (-1)R3

$\left[\begin{array}{ccc|c}
1 & 0 & 0 & 33\
0 & 0 & 1 & 25\
0 & 1 & 0 & 12
\end{array}\right]$

Longest = 33cm
Medium = 25cm
Shortest = 12cm

shamil98 · Answer

What do R1 R2 R3 values mean?

e.mccormick · Answer

Row 1, 2, and 3.

e.mccormick · Answer

matrices use RC notation, Row by Column.  So position 1,2 is row 1, column 2.  The R and C then get reused a lot of places.... but some books like M and N.

shamil98 · Answer

Why is R1 multiplied by 1/2? I never took algebra 2 lol.

e.mccormick · Answer

To get the pivot points to 1.  The left hand side wants 1 in each column, known as the pivots.  If you have onely one pivot at 1 in each row, then the right hand side is the solution to the system.

e.mccormick · Answer

Well, one in each row and one in each column, I should say.... so one value at 1 for each.

shamil98 · Answer

Just a question where does the 66 come from ?..

e.mccormick · Answer

70+(-4)

Here is a more detailed explanation, but only 4 pages so reasonably short:
www.epcc.edu/tutorialservices/valleverde/Documents/Gauss-Jordan_Method.pdf

It includes another worked example.

e.mccormick · Answer

Was gonna share this with that guy after you worked the solution with them,.... but that question sort of died.  LOL.  So thought I would at least share it with you so you could see another way.

shamil98 · Answer

Yeah, he never replied haha

e.mccormick · Answer

Matrices can also be really helpful in solving some calculus problems.  Another neat tool from Linear Algebra is the determinant, which can be used to easily find the area of an ellipse, volume of a parallelopiped, see if there are solutions to complex systems, and so on.