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Good Day Everyone,
There is a new way and faster methods of solving linear equation ( Matrices) involving 2, 3,4 unknowns.
I present to you, Adebayo Kassim Picking Methods for Matrices,linear equation, Matrix etc.
Adebayo Kassim Picking Methods is a methods for solving linear equation.it is a better alternative to crammer's rule because it is faster and it is easier to arrange.
I attached with this an except from the book. Just go through it and see that it works perfectly.
Yours Sincerely
Adebayo Kassim

‎How To Solve Simultaneous Equations, Matrices Unknowns Using Adebayo Kassim Picking Methods (Pick Direct Methods)


‎Ensure the two equations is equal to zero ie ax1 + by1 + c = 0, ax2 + by2 + c = 0. Pick the first two column coefficient that is first and second and then find the determinants (d). Pick the next two column coefficient ie second and third and then find the determinants (d1). Pick the next two column coefficient ie Third and first and find the determinants (d2)
‎
‎X = d1/ d
‎
‎Y= d2/ d
‎
‎Example: Solve for x and y in the equation
‎5x - 3y = 11
‎3x - y = 9
‎
‎[b]Solution
‎5 x - 3 y - 11= 0
‎3 x - y - 9 = 0
‎
‎D= determinants of the first two column coefficient, that is first and second column coefficient = (5)(-1) - (3) (-3) = - 5 + 9 = 4
‎
‎D1= determinants of the second and third column coefficient = (-3)(-9) - (-1)(-11)
= 27 - 11=16
‎
‎D2= determinants of the third and first column coefficient = (-11)(3) - (-9)(5)
= - 33 + 45 =12
‎
‎X = D1/D = 16/4 = 4
‎
‎Y= D2/D = 12/4 = 3

How To Solve Simultaneous Equations, Matrices Unknowns Using Adebayo Kassim Picking Methods (Pick Direct Methods) for 3 x 3.

PICK DIRECT METHODS
Ensure the equations is equal to zero
ie ax + by + cz + d = 0,

Pick the first three column coefficient that is first, second and third then find the determinants (d). Pick the next three column coefficient ie second, third and constant coefficient, then find the determinants (d1). Pick the next three column coefficient ie Third, constant and first column coefficient and find the determinants (d2). Pick the next three coefficient ie constant, first and second column coefficient then find the determinants (d3)

‎X = - d1/ d
‎Y= + d2/ d
Z = - d3/ d

Example: Solve the equation
X + Y - Z = 6
X - Y + Z = 2
X + 2Y - Z = 2

Ensure the equations is equal to zero
ie ax + by + cz + d = 0,
Therefore,
X + Y - Z - 6 = 0
X - Y + Z - 2 = 0
X + 2Y - Z - 2 = 0

Pick the first three column coefficient that is first, second and third then find the determinants (d).

d= 1( 1 - 2 ) - 1 ( - 1 - 1) - (2 + 1)
= 1(-1) - 1( -2) -1 (3)
= -1 + 2 - 3
= - 2

Pick the next three column coefficient ie second, third and constant coefficient, then find the determinants (d1).
d 1= 1( - 2 - 2) + 1( 2 + 4 ) - 6 (1 - 2 )
= 1( - 4) + 1 (6) - 6 (-1)
= - 4 + 6 + 6
= 8

Pick the next three column coefficient ie Third, constant and first column coefficient and find the determinants (d2).
d2= -1( -2 + 2) + 6 (1 + 1) + 1(-2 -2)
= -1(0) + 6(2) + 1(-4)
= 0 + 12 - 4
= 8
Pick the next three coefficient ie constant, first and second column coefficient then find the determinants (d3)
d3 = - 6( 1 + 1) - 1 ( - 2 + 2 ) + 1( -2 + 2 )
= - 6 ( 2 ) - 1 (0 ) + 1 (0)
= -12

X = - d1/ d = - ( 8 )/ - 2 = -8/ -2 = 4
Y = + d2/d = 8/ -2 = - 4
Z = - d3/d = - ( - 12) / - 2 = 12/ -2 = - 6
X = 4 , Y = - 4 , Z = - 6


Example: Solve the equation
3x - 2y + Z = 8
6x - y + Z = 13
X + Y + Z = 6
Solution
3X - 2Y - Z - 8 = 0
6X - Y + Z - 13 = 0
X + Y + Z - 6 = 0
Pick the first three column coefficient ie C1, C2 , and C3. Find determinants D.
Therefore, D = ( - 3 - 2 + 6) - ( -1 + 3 -12)
= (1) - (- 10)
= 11
Pick the next three column coefficient ie C2, C3 and constant C4. Find the determinants D1
Therefore, D1 = (12 - 13 + 8 ) - ( -8 +26 + 6)
= 7 - 24
= -17
Pick the next three column coefficient ie C3, constant coefficient and C1. Find determinants
D2= ( -13 - 48 - 18 ) - (- 39 - 36 - 8 )
= - 79 + 83
= 4
Pick the next three column coefficient ie constant coefficient C4, then C1, and C2. Find determinants.
D3 = ( - 48 + 18 + 26) - (72 + 8 -39)
= ( - 4) - 41
= - 45

X = - D1/ D = - (-17)/11 = 17/11

Y= + D2/ D = 4/11

Z = - D3/D = - ( - 45)/ 11 = 45/11

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