 Hi and welcome to the session, let's work out the following question. The question says, using matrix method solve the following equations, 2x minus 3y is equal to 1, x plus 3z is equal to 11 and x plus 2y plus z is equal to 7. Let's start with the solution to this question. First of all, let's write the given equations in matrix form we will have. 2 minus 3, 0, 1, 0, 3, 1, 2, 1, multiplied by matrix x, y, z is equal to the matrix 117. Now let a into x be equal to b, this implies that x is equal to a inverse b if mod a is not equal to 0, we call this 1. Now mod a is equal to the matrix 2 minus 3, 0, 1, 0, 3, 1, 2, 1, this is equal to 2 into 0 minus 6 plus 3 into 1 minus 3, this is equal to minus 12 minus 6 and this is equal to minus 18 which is not equal to 0 as determinant a, this is also determinant a, so as determinant a is not equal to 0, therefore a inverse will exist. This implies that a inverse is equal to 1 upon determinant a into adjoint a, now adjoint a is equal to the matrix C11, C21, C31, C12, C22, C32, C13, C23, C33 where C11 is this into this minus this into this, similarly C21 is minus of this into this minus this into this, C31 is this into this minus this into this and so on for other elements also. So solving this we get the matrix minus 6, 3 minus 9, 2, 2 minus 6, 2 minus 7, 3. Now since a inverse is 1 upon determinant a into adjoint of a, so a inverse is equal to 1 upon minus 18 into matrix minus 6, 3 minus 9, 2, 2 minus 6, 2 minus 7, 3. Now putting the value of a inverse in x equals to a inverse b we get the matrix x, y, z is equal to minus 1 by 18 into the matrix minus 6, 3 minus 9, 2, 2 minus 6, 2 minus 7, 3 into the matrix b that is 117. This implies that the matrix x, y, z is equal to minus 1 upon 18 into the matrix minus 6 plus 33 minus 63. In the second row we have 2 plus 22 minus 42 in the third row we have 2 minus 77 plus 21. This simplifies to minus 1 by 18 into the matrix minus 36 minus 18 minus 54 and this further simplifies to the matrix 2, 1, 3. So our answer to this question is x is equal to 2, y is equal to 1 and z is equal to 3. I hope that you understood the solution and enjoyed the session. Have a good day.