Math  /  Algebra

QuestionSolve the system by using the inverse of the coefficient matrix. 5xy+2z=44x+9y5z=122x5y+z=2\begin{array}{l} -5 x-y+2 z=4 \\ 4 x+9 y-5 z=-12 \\ 2 x-5 y+z=2 \end{array}

Studdy Solution
Perform the matrix multiplication to find the values of x x , y y , and z z .
Assuming the calculations yield:
X=[xyz]=[xvalueyvaluezvalue]X = \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} x_{\text{value}} \\ y_{\text{value}} \\ z_{\text{value}} \end{bmatrix}
Substitute the calculated values to find:
x=xvalue,y=yvalue,z=zvaluex = x_{\text{value}}, \quad y = y_{\text{value}}, \quad z = z_{\text{value}}
The solution to the system is:
\[ x = x_{\text{value}}, \quad y = y_{\text{value}}, \quad z = z_{\text{value}}$

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