# Given a linear system of equations below. The matrix equation of the linear system is given

Forms of linear equations

Given a linear system of equations below. The matrix equation of the linear system is given by: (see image)
Given a linear system of equations below.The matrix equation of the linear system is given by:$$Ax=b$$.The determinant of A is 8.Using Cramers's rule find the value for x.
$$x+3y+4z=3$$
$$2z+6y+9z=5$$
$$3x+y-2z=7$$

2021-01-11

Consider the provided system of equation
$$x+3y+4z=3$$
$$2z+6y+9z=5$$
$$3x+y-2z=7$$
The matrix equation of the linear system is given by,
$$AX=b$$
Where, $$A[(1,3,4),(2,6,9),(3,1,-2)]$$
given, $$|A|=8$$
Find the value of x by using cramer's rule
$$x=\frac{|D_x|}{|D|}$$
here, $$D_x=[(3,3,4),(5,6,9),(7,1,-2)]$$
and, $$|D|$$ is the determinant of the matrix A
Since,when system of equation as,
$$a_1x+b_1y+c_1z=d_1$$
$$a_2x+b_2y+c_2z=d_2$$
$$a_3+b_3+c_3z=d_3$$
Then, $$D_x=[(d_1,b_1,c_1),(d_2,b_2,c_2),(d_3,b_3,c_3)]$$
Now, the value of x find as,
$$x=\frac{|D_x|}{|D|}$$
$$=|(3,3,4),(5,6,9),\frac{7,1,-2}{|A|}$$
$$=\frac{(-36+20+189)-(168+27-30)}{8}$$
$$=\frac{173-165}{8}$$
$$=\frac{8}{8}$$
$$=1$$
Thus, $$x=1$$