 Hi and how are you all today? My name is Priyanka and let us discuss this question. It says using matrix method Solve the following system of linear equations. Now here we have the linear equations as x plus y plus z is equal to 3, 2x minus y plus z is equal to 2, x minus 2y plus 3z is equal to 2. Now here, here we have matrix A written as coefficient of x in the first equation, 1, coefficient of x in the second equation as 2 and coefficient of x in the third equation as 1 and then we have in the second column coefficient of y, that is 1, then minus 1 and so on, minus 2 and coefficient of z in the third column. We have matrix zx as x, y, z and matrix B equal to 3, 2, 2, right? So the following system of linear equation can also be written as matrix A into matrix X is equal to matrix B. This implies matrix X is equal to A inverse. Now here, let us find out the value of the determinant A that is equal to 1 into minus 3 plus 2 minus 1 into 6 minus 1 plus 1 into minus 4 plus 1, right? Let us solve it out. So we have minus 1 minus 5 minus 3 which is for the v equal to minus 9. Let us find out a joint A for that. We need to find out A11 that is minus 1 and so on. Then 8, 2, 1 minus 5 8, 2, 2 as 2, 8, 2, 3 as 3. And then lastly, A31, A32, A33 which is 2, 1, minus 3. So therefore, we can write down a joint A as minus 1, minus 5, minus 3, minus 5, 2, 3, 2, 1, minus 3. Now this is our adjoint A. This is a known formula for us. So we have the value of determinant A is minus 9. So we have minus 1 by 9 into adjoint A. Now substituting this value that is the value of A inverse above we had x equal to A inverse B, right? So now we have x equal to minus 1 by 9 writing down a joint A into B that is 3, 2, 2. Now on solving out we have minus 1 by 9 on solving these two matrix, we have minus 9, minus 9, minus 9, which on dividing by minus 1 by 9 gives us 1, 1, 1, right? So therefore x equal to y equal to z equal to 1 is the required solution to the given question. So hope you understood it well and have a nice day.