 Hi and how are you all today? The question says using matrix method, solve the given linear equations. The linear equations which are given to us are 2x minus y plus z is equal to minus 3, 3x minus z is equal to minus 8, 2x plus 6y is equal to 2. So let's proceed on with the solution by rewriting the given linear equations once again. We have 2x minus y plus z is equal to minus 3. This can be written as 3x plus 0y minus z is equal to minus 8, right? And this can be written as 2x plus 6y plus 0z is equal to 2. Now we have a into x equal to b where matrix a is equal to 2, 3, 2, 2, 3, 2 that are the coefficients of x. Then we'll write the coefficients of y minus 1, 0, 6 and then the coefficients of z that are 1 minus 1, 0. And we have matrix x as x, y, z and matrix b as minus 3, minus 8 and 2. Now let us first find out the value of determinant a. It is equal to 2 bracket 0 plus 6 plus 1 bracket 0 plus 2 plus 1 bracket 18 minus 0. That is equal to 32 which means it is not equal to 0. So a inverse exists and is given by 1 upon determinant a, a joint a. That is equal to 1 upon the value of determinant a is coming out to be 32 into a joint a which we have found out as 6 minus 2, 18, 6 minus 2, minus 14 and 1, 5 and 3. So now let us substitute the value of this a inverse from second in here. x is equal to a inverse b. So we have x equal to a inverse. Let me write it down again into b. That is minus 3 minus 8, 2. Now on solving it we have in place of x we write the matrix x is equal to on solving it 1 by 32. On solving these two matrices we have minus 64, 32, 64. That gives us the answer as minus 2, 1 and 2 which is equal to x, y, z. So therefore we have the answer as the value of x as minus 2, y as 1 and z as 2. Right, so this completes the solution. Hope you understood it well and enjoyed it too. Have a nice day.