Answer:
Hence, the determinant of the coefficient matrix of the system is:
65
Step-by-step explanation:
We are given a system of linear equation in terms of variable x,y and z as:
\(-3x+2y-6z=5\)
\(-7x+9y-z=4\)
\(-2x+5y+2z=9\)
Hence, the coefficient matrix that is obtained with the help of these system of equation let us denote by A is:
\(A=\left[\begin{array}{ccc}-3&2&-6\\-7&9&-1\\-2&5&2\end{array}\right]\)
Now let us find the determinant of the matrix by expanding along row 1 as:
\(=-3(2\times 9-(1\times (-5))-2(-7\times 2-(-1)\times (-2))-6(-7\times 5-9\times (-2))\\\\\\=(-3)\times 23-2\times (-16)-6\times (-17)\\\\=-69+32+102\\\\=65\)
Hence, the determinant is:
65
