Question

What is the determinant of the coefficient matrix of the system

Answer 1

Hence, the determinant of the coefficient matrix of the system is:

65

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* 9-(1* (-5))-2(-7* 2-(-1)* (-2))-6(-7* 5-9* (-2))\\\\\\=(-3)* 23-2* (-16)-6* (-17)\\\\=-69+32+102\\\\=65`

Hence, the determinant is:

65