What is the determinant of the coefficient matrix of the system

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

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We are given a system of linear equation in terms of variable x,y and z as:

Hence, the coefficient matrix that is obtained with the help of these system of equation let us denote by A is:

Now let us find the determinant of the matrix by expanding along row 1 as:

              Hence, the determinant is:

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