 Hi, and welcome to our session. Let us discuss the following question. The question says, using matrix method, solve the following system of linear equation. x plus 2y minus 3z equals to minus 4. 2x plus 3y plus 2z equals to 2. 3x minus 3y minus 4z equals to 11. Let's now begin with the solution. Now, given system of equations can be written as equals to b, where 2 to 3 by 3 matrix in which elements are coefficient of x, y, and z. That is 1, 2, 3, 2, 3, minus 3, 2, minus 4. x is equal to column matrix, which consists of variables x, y, and z. b is also equal to a column matrix in which elements are minus 4 to 11. It's a non-singular matrix or singular matrix. So let us first find determinant of a is equal to 1 into determinant of 3 minus 3, 2, minus 4, minus 2 into determinant of 2, 3, 2, minus 4, minus 3 into determinant of 2, 3, 3, minus 3. Now, this is equal to 1 into minus 12 plus 6, minus 2 into minus 8, minus 6, minus 3 into minus 6, minus 9. This is equal to minus 6, minus 2, into minus 40, minus 3, into minus 50. This is equal to minus 6 plus 28, plus 45, so to minus 6 plus 73. And this is equal to 67, which is not equal to 0. So since determinant of a is not equal to 0, the non-singular matrix exists. 1 into determinant of 1 into minus 12 into minus a1, 3 is equal to minus 1 to the power 1 plus 3 into 2, minus 1, minus 1 to the power 3, plus 2, minus 1, into 14, 67, plus 67, is equal to column matrix in which 3, minus 2, y, 3, y equals to minus 2, and z equation is x equals to 3, y equals to minus 2, and z equals to y. This completes the section by and thank you.