 Hello and welcome to the session. I am Deepika here. Let's discuss the question. Solve system of linear equations using matrix method 2x minus y is equal to minus 2, 3x plus 4y is equal to 3. Solution. The given system of equations can be written in the form Ax is equal to b where a is equal to 2 minus 1, 3, 4, x is equal to xy, b is equal to minus 2 and 3. See that determinant of a is equal to a plus 3 which is equal to 11. This implies determinant a is not equal to 0. Hence this non-singular inverse exists. Now we will first find out the inverse. For inverse, we will find out adjoint of a. So adjoint a can either be found by taking the co-factor of each element and then form the matrix using the co-factors and then taking its transpose or we can find by interchanging the elements a11 and a22 that is adjoint a is equal to and changing the sign of these two elements that is 1 and minus 3. Now we know that a inverse is equal to 1 over determinant a into adjoint a. This implies a inverse is equal to 1 over 11 into 4, 1 minus 3, 2. Now we have written our given system of linear equation in the form Ax is equal to b. Pre-multiply by a inverse we get a inverse Ax is equal to a inverse b. This implies is equal to a inverse b which is equal to a inverse is of 1 over 11, 4 minus 3, 1, 2 into b is our minus 2, 3. This is equal to 4 into minus 2. This is minus a plus 3 and minus 3 into minus 2, 6 plus 6. This implies our x is, xy is equal to 1 by 11 minus 5 and 12. So by quitting the corresponding elements we get x is equal to minus 5 by 11 and y is equal to 12 by 11. Hence we have solved the above system of linear equations using map technique and our answer is x is equal to minus 5 by 11 and y is equal to 12 by 11. I hope the question is clear to you. Bye and have a good day.