1 3 9 7 x 7 6 4 6 3 3 8 1 x Solutionlet X x1 x2 x3 x4 1

[1 -3 -9 7] x + [7 6 4 -6] = [-3 -3 8 1] x = [ ]

Solution

let X = x1    x2

            x3 x4

[1   -2] * [ x1     x2]       +[7 6]       = [-3     -3] [x1   x2]

-9    7       x3      x4         4    -6              8       1   x3    x4    // matrix multiplication

[x1 - 2x3      x2 - 2x4 ]      + [7      6]       =       [-3x1 - 3x3      -3x2 - 3x4]        

-9x1 + 7x3    -9x2 + 7x4          4      -6                  8x1 + x3         8x2 + x4             

[x1 -2x3 +7           x2 -2x4 + 6]             =  [ -3x1 -3x3            -3x2 - 3x4]

-9x1+7x3 +4       -9x2 +7x4 -6                  8x1 + x3              8x2 + x4

x1 -2x3 +7 = -3x1 -3x3           => x1 + 3x1 = -3x3 +2x3 -7 => 4x1 = -x3 -7         (1)

x2 -2x4 + 6 = -3x2 -3x4    =>    4x2 = -x4 -6          (2)

-9x1 +7x3 +4 = 8x1 +x3 => 17x1 = 6x3  + 4          (3)

-9x2 +7x4 -6 = 8x2 +x4    => 17x2 = 6x4 - 6         (4)

from (1) and (3)

17x1 = 6x3 + 4       (3)               subtituting the value of x3 from (1)

17x1 = 6(-4x1 -7) + 4

17x1 = -24x1 -42 +4

41x1 = -38

x1 = -38/41

therefore from (1)

x3 = -4x1 - 7

x3 = -4*(-38/41) -7

x3 = 152/41 - 7

x3 = -135/41

from (2)and (4)

17x2 = 6x4 - 6       (4)     // subtituting the value of x4 from (2)         x4 = -4x2 - 6

17x2 = 6(-4x2 -6 ) -6

17x2 = -24x2 -36 -6

41x2 = -42

x2 = -42/41

from (2)

x4 = -4(-42/41) - 6

x4 = 168/41 -6

x4 = -78/41

therefore X =    -38/41          -42/41

                        -135/41         -78/41