‘Mamata withdraws support to UPA government’ this is the front
page column in today’s news paper ‘The Hindu’. The part of the news attracted me more is a
table named ‘How the arithmetic works’ right at the centre of the article.
UPA – Trinamool

246

UPA – Trinamool + SP + BSP + RJD

293

UPA – Trinamool  SP + BSP + RJD

271

UPA – Trinamool  SP  BSP + RJD

251*

UPA – Trinamool + SP + BSP + RJD +JD(S)

296

UPA – Trinamool  SP  BSP + RJD +JD(S)

253

*original value given
in the article is 250. It is changed for the ease of calculations
Here I do not want to contemplate on the fate of UPA in case
Mamata Deedi withdraws support or Lalluji & Malluji extend it
or what so ever. What I see is this: six relationships are given between memberstrengths
of six parties. Can’t we find the memberstrengths of each party? Let us give a
try..
First let us write down these in the form of equations:
UT = 246 (1)
UT+S+B+R = 293 (2)
UTS+B+R = 271 (3)
UTSB+R = 251 (4)
UT+S+B+R+J = 296 (5)
UTSB+R+J = 253 (6)
Now let us solve:
(2)(1) gives => S+B+R = 47 (7)
(3)(1) gives => S+B+R = 25 (8)
(4)(1) gives => SB+R = 5 (9)
(7)(8) gives => 2S = 22 => S = 11
(8)(9) gives => 2B = 20 => B = 10
(7)+(9) gives => 2R = 52 => R = 26
(5)  (2) gives => J = 3
By now, we have got strengths of four parties SP, BSP, RJD and JD(S). But
can we do it for UPA and Trinamool?
We can’t. With the given set of data it is not possible. Even
though six equations in six unknowns are given, we cannot solve for all the six
variables. Why so?
Here U and T are represented together as (UT) in all the
equations. It is represented as a single entity and the value of that entity (UT)
is only known. Even though we are provided with n number of such equations we
can’t find the individual value of either U or T. And one more thing, only one
of the equations 5 or 6 is enough to find the value of J and the other equation
is useless (‘redundant’ in mathematical sense). So effectively there are less
than six equations.
(To prove this mathematically, mathsavvies can try out one
of the standard methods: Cramer’s or Matrix or Rank method. Here Rank
method is suitable as in the other methods it involves dealing with determinant
of 6X6 matrix, which is difficult)
Click on the compressed sheet down here for the mathematical proof by Rank method:
Click on the compressed sheet down here for the mathematical proof by Rank method:
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