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

Question

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: $A x = b$ .The determinant of A is 8.Using Cramers's rule find the value for x.
$x + 3 y + 4 z = 3$
$2 z + 6 y + 9 z = 5$
$3 x + y - 2 z = 7$

Answer 1

Consider the provided system of equation
$x + 3 y + 4 z = 3$
$2 z + 6 y + 9 z = 5$
$3 x + y - 2 z = 7$
The matrix equation of the linear system is given by,
$A X = b$
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,
$a_{1} x + b_{1} y + c_{1} z = d_{1}$
$a_{2} x + b_{2} y + c_{2} z = d_{2}$
$a_{3} + b_{3} + c_{3} z = d_{3}$
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, $x = 1$

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

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