Problem #$1.(35$ points$).$ For the set of linear algebraic equations in Eq$.(1)$:

$8x_1+4x_2-x_3=11$

$-2x_1+5x_2+x_3=4$

$2x_1-x_2+6x_3=7$

$(10$ points$).$ Write the elements of the matrix corresponding to:

a$.(4$ points$)$ The matrix of coefficients $A,$

b$.(3$ points$)$ The vector of unknowns $\{x\}$ and,

c$.(3$ points$)$ The independent terms column vector $\{b\}.$

$(10$ points$).$ Calculate the determinant of the matrix A given in Eq$.(1).$

$(10$ points$).$ Use the Elimination Method to solve the system of linear simultaneous equations. Show all the

steps of the computation.

$(5$ points$)$ Verify your results by substituting $\{x\}$ into each equation given in Eq$.(1).$