 Let us now begin with the solution. Now, given equations and we return the three matrix in which elements are 1, 1, minus 1, 3, 1, minus 2, 1, minus 1, minus 1. This matrix consists of all coefficients of x, y, and z. X is equal to column matrix in which elements are x, y, and z. V is also equal to column matrix in which elements are 1, 3, minus 1. Determinant of A equal to 1 into determinant of 1, minus 1, minus 2, minus 1. Minus 1 into determinant of 3, 1, minus 2, minus 1. Minus 1 into determinant of 3, 1, 1, minus 1. Now, this is equal to 1 into minus 1, minus 2, minus 1, into minus 3, plus 2, minus 1, into minus 3, minus 1. This is equal to minus 3, minus 1, into minus 1, minus 1, into minus 4. This is equal to minus 3, plus 1, plus 4. And this is equal to 2, which is not equal to 0. So, as determinant of A is not equal to 0s, therefore A is a non-singular matrix. Since non-singular A inverse exists, so let us now find A inverse. For determining A inverse, we have to first find cofactors of all elements of matrix A. A11 is equal to minus 1 to the power 1 plus 1 into determinant of 1, minus 1, minus 2, minus 1. This is equal to 1 into minus 1, minus 2, and this is equal to minus 3. 2 is equal to minus 1 to the power 1 plus 2 into determinant of 3, 1, minus 2, minus 1. This is equal to minus 1 into minus 3, plus 2, and this is equal to 1. A13 is equal to minus 1 to the power 1 plus 3 into determinant of 3, 1, 1, minus 1. Now this is equal to 1 into minus 3, minus 1, and this is equal to minus 4. 2, 1 is equal to minus 1 to the power 2 plus 1 into determinant of 1, minus 1, minus 1, minus 1. And this is equal to minus 1 into minus 1, minus 1, and this is equal to 2. A22 is equal to minus 1 to the power 2 plus 2 into determinant of 1, 1, minus 1, minus 1. This is equal to 1 into minus 1, and this is equal to 0. Now A23 is equal to minus 1 to the power 2 plus 3 into determinant of 1, 1, 1, minus 1. And this is equal to minus 1 into minus 1, minus 1, and this is equal to minus 1 to the power 3 plus 1 into determinant of 1, 1, minus 1, minus 2. This is equal to 1 into minus 2 plus 1. This is equal to minus 1 equal to to the power 3 plus 2 into determinant of 1, 3, minus 1, minus 2. This is equal to minus 1 into minus 2 plus 3. This is equal to minus 1. Now A33 is equal to minus 1 to the power 3 plus 3 into determinant of 1, 3, 1, 1. And this is equal to 1 minus 3, and this is equal to minus 2, a joint A. Now a joint A is equal to 3 by 3 matrix in which elements are minus 3, 2, minus 1, 1, 0, minus 1, minus 4. Now A inverse is equal to 1 by determinant of A into a joint. D implies x is equal to A inverse p. Now A inverse is equal to this, and v is equal to column matrix in which elements are 1, 3, minus 1. Now this is equal to 1 by 2 into column matrix in which elements are minus 3 plus 6 plus 1, 1 plus 0 plus 1, minus 4 plus 6 plus 2. Now this is equal to 1 by 2 into column matrix in which elements are 4 to 4. And this is equal to column matrix in which elements are 2, 1, 2. x is also equal to column matrix in which elements are x, y, and z. Now this implies x is equal to 2, y is equal to 1, and z is equal to 2. Hence I require the answer is x equals to 2, y equals to 1, and z equals to 2. So this completes the session by and take care.