 Hello and welcome to the session. I am Deepika here. Let's discuss a question. Solve system of linear equations using matrix method 5x plus 2y is equal to 3. 3x plus 2y is equal to 5. Let's start the solution solution The given system of equations can be written in the form to be where a is equal to 5, 2, 3, 2 x is equal to x, y and z is and b is equal to 3, 5. Determinant a is equal to 10 minus 6 which is equal to 4 that is not equal to 0. This implies a is non-singular inverse exist. Now adjoint a is equal to let us interchange a11 and a22 we get 2, 5 or change the sign of 2 and here also minus c or we can find out adjoint a by taking the co-factors of each element and then form the matrix using the co-factor then take its transpose we will get that adjoint a therefore a inverse is equal to 1 over determinant a into adjoint a this implies a inverse is equal to 1 over 4 into 2 minus 3 minus 2, 5. Now ax is equal to b implies a inverse a x is equal to a inverse b by pre multiplication by a inverse this implies x is equal to a inverse b this implies x is equal to a inverse b again this implies x is equal to not a inverse is 1 by 4 into 2 minus 3 minus 2, 5 into b is r 3, 5. This implies x is equal to 1 by 4 into 2 3's are 6 minus 10 minus 9 plus 25 which is equal to 1 by 4 minus 4 and 16 this is again equal to minus 1 and 4. This implies xy is equal to minus 1, 4 by equating the corresponding elements we get x is equal to minus 1 and y is equal to 4 so we have solved the above system of linear equations using matrix method and our answer is x is equal to minus 1 and y is equal to 4. I hope you have enjoyed the session. Bye and take care