 Hi and welcome to the session. I am Deepika here. Let's discuss the question find the values of x y and z from the following equations a 2 by 2 metrics whose elements are x plus y 2 5 plus z x y is equal to metrics 6 to 5 8. In this question, we will use a property of equal matrices Which means if two matrices are equal, then their corresponding element must be equal So we will use this property to solve the above question. Let's start the solution by equality of two matrices equating the corresponding elements we get plus y Is equal to 6. Let us take it as a 5 plus z is Equal to 5. Let us take it as b xy is equal to a Let us take it as c Now we will solve these equations From b we have 5 plus z is Equal to 5. This implies that this is equal to 0 now we will solve a and see From a we have x plus y is equal to 6 and from c we have xy is equal to 8 We have x minus y whole scale is equal to x plus y whole scale minus 4 x y Substitute the value of x plus y that is x plus y is equal to 6 and the value Of x y from c that is x y is equal to 8 in this formula we get x minus y whole scale is equal to 6 square minus 4 into 8 which is equal to 36 minus 32 Therefore x minus y square is equal to 4 which implies x minus y is equal to plus minus 2 Now we have two values of x minus y that is x minus y is equal to plus 2 and x minus y is equal to minus 2 if x minus y is equal to plus 2 then from a we have x plus y is equal to 6 on adding These equations we get x is equal to 8 this implies x is equal to 4 Put x is equal to 4 In a we get y is equal to 2 So in this case that is if x minus y is equal to 2 our solution is x is equal to 4 Y is equal to 2 and z is equal to 0 now consider the second case where x minus y is equal to minus 2 if X minus y is equal to minus 2 from a we have x plus y is equal to 6 On adding this we get 2x is equal to 4 this implies x is equal to 2 put x is equal to 2 in equation a in x plus y is equal to 6 we get y is equal to 4 So in this case our solution is x is equal to 2 y is equal to 4 z is equal to 0 Hence we get two solutions for x y z that is x is equal to 4 y is equal to 2 z is equal to 0 or x is equal to 2 y is equal to 4 Z is equal to 0. This is our answer. I hope you have understood the question by and have a good day