 Hello and welcome to the session, I am Deepika here. Let's discuss the question. Solve system of linear equations using matrix method, 5x plus 2y is equal to 4, 7x plus 3y is equal to 5. Let's start the solution. The given system of equations can be written in the matrix form. Ax is equal to b where, a is equal to 5, 2, 7, 3, x is equal to xy, b is equal to 4, 5. Now determinant a is equal to 15 minus 14 which is equal to 1. This implies determinant a is not equal to 0. Hence, e is non-singular because determinant of a is equal to 1 which is not equal to 0. So, has a unique solution. Now we will find the solution by the matrix method. Since a is non-singular, so its inverse exists. So for a inverse let us first find out adjoint of a. So adjoint of a is equal to, we know that the adjoint of a, if a is a square matrix of order 2 by 2, so adjoint a can be obtained by interchanging a11 and a22 that is like this and by changing signs of a12 and a21 that is minus 2 and minus 7. Or we can find out the adjoint by first find out the co-factors of each element then form the matrix by the co-factors and take the transpose of that matrix we will get the adjoint a. Now a inverse is equal to 1 over determinant a into adjoint a which is equal to 1 over 1 into 3 minus 7 minus 2 5. x is equal to b implies a inverse into a x is equal to a inverse b pre-multiplying both sides by a inverse. This implies ix is equal to a inverse b. Now a inverses are b minus 7 minus 2 5 and b is 4 5 which is equal to, this implies x is equal to 12 minus 10 minus 28 plus 25 which is equal to 2 minus 3. Now x is equal to xy this is equal to 2 minus 3. Now equating the corresponding elements we get x is equal to 2 and y is equal to minus 3. So we have solved above system of linear equations using matrix method and our answer is x is equal to 2 and y is equal to minus 3. I hope the question is clear to you. Bye and have a good day.