Use Gramers Rule to solve for x1 in the following linear sys

Use Gramer\'s Rule to solve for x_1 in the following linear system of equations

Solution

This can be represented in Matrix form as
[ 1 4 2 ] [1]
[ 2 -1 2] [2]
[-3 2 -3] [1]

Determinant of the given coefficient matrix is =
1(3-4) -4(-6+6)+ 2(4-3) = -1+2=1;
D_x1 will thus be given by replacing the first column with the constant matrix:

[ 1 4 2 ]
[ 2 -1 2]   
[1 2 -3]
Te determinant of D_X1 = 1(3-4) -4(-6-2) + 2(4+1) = -1+32 +10 = 41

Thus x₁ is given by D_x1 / D_x = 41/1 = 41

So, using Cramer\'s rule x₁ is given as = 41