 Hi and welcome to the session. I am Deepika here. Let's discuss the question. Solve system of linear equations using matrix method. x minus y plus z is equal to 4. 2x plus y minus 3z is equal to 0. x plus y plus z is equal to 2. Let's start the solution. Solution. The given system of equations that is the linear equation can be written in the form is equal to b where is equal to 1 minus 1 1 2 1 minus 3 1 1 1 equal to x y z and b is equal to 402. See that determinant a is equal to 1 into 1 plus 3 of minus 1 into plus 1 into 2 minus 1. Which is equal to 1 into 4 plus 1 into 5 plus 1 into 1. That is equal to 4 plus 5 plus 1 which is equal to 10 and it is not equal to 0. This as determinant a is not equal to 0. This implies a is non-singular and so its inverse exists. Now we will find out the inverse of a. For inverse of a we will first find out adjoint it. Now co-factor of 1 is equal to minus 1 raise to power 1 plus 1 into 1 plus 3. That is equal to co-factor of 1 is equal to minus 1 raise to power 1 plus 1 into 1 plus 3 which is equal to 4. Similarly co-factor of minus 1 is equal to minus 1 raise to power 1 plus 2 into 2 plus 3 which is equal to minus 5. Similarly we can find out the co-factors of each and every element which is as follows. Now the matrix formed by by the above co-factors is equal to minus 5 1 2 0 minus 2 2 5 3. Now adjoint a is equal to transpose of this matrix that is 4 minus 5 1 2 0 minus 2 2 5 3 which is equal to 4 minus 5 1 2 0 minus 2 2 5 3. Therefore a inverse is equal to 1 over determinant a into adjoint a which is equal to 1 over 10 into 4 minus 5 1 2 0 minus 2 and 2 5 3. Now a inverse now we have ax is equal to b implies a inverse ax is equal to a inverse b pre-multiplying by a inverse this implies ix is equal to a inverse b which implies our ax is equal to a inverse b as identity matrix into matrix is equal to the matrix. This implies this is equal to our a inverse is 1 by 10 into 4 minus 5 1 2 0 minus 2 2 5 3 into b is our 4 0 2. This implies ax is equal to 1 by 10 into 4 4s are 16 plus 0 plus 4 minus 20 plus 0 plus 10 and 1 into 4 4 minus 0 plus 6 which is equal to 1 by 10 into 20 minus 10 and 10 this is again equal to 2 minus 1 1 this implies x y z is equal to 2 1 2 minus 1 and 1 by quitting the corresponding elements we get x is equal to 2 y is equal to minus 1 and z is equal to 1 hence we have solved the system of linear equations using matrix method and our answer is x is equal to 2 y is equal to minus 1 and z is equal to 1 I hope the question is clear to you bye and have a good day.