 Hi and welcome to the session. I am Deepika here. Let's discuss the question from the chapter determinants So let's start the question by using properties of determinants show that Determinant y plus k y y y y plus k y Y y y plus k is equal to k square into 3 y plus k So let's start the solution Just look at the right-hand side. We want k square into 3 y plus k now Look at the left-hand side 3 y plus k can be obtained if you will add R1 plus R2 plus R3 so Now start we have on our left-hand side is equal to y plus k y y Y y y plus k y Y y y plus k by applying one goes to R1 plus R2 Plus R3 we get Our left-hand side is equal to now this is 3 y plus k Again here we get 3 y plus k and 3 y plus k row 2 and row 3 is as it is Now clearly 3 y plus k is common in our ones. So by taking out common factor factor 3 y plus k Common from R3 we get our left-hand side is equal to 3 y plus k into 1 1 1 y y plus k Y again y y y plus k now by applying 3 goes to R3 minus R2 We get Our left-hand side is equal to 3 y plus k now 1 1 1 Y y plus k Y now R3 goes to R3 minus R2. So this is 0 This is minus k and this is k now clearly case Common in R3. So by taking out factor and from R3 Our left-hand side is equal to 3 y plus k Into k so 1 1 1 y into y plus k into y 0 this is minus 1 and 1 Now by applying 2 goes to C2 plus C3 We get our left-hand side is equal to 3 y plus k Into k Now this is 1 C1 is as it is 1 y 0 now C2 is C2 plus C3 So this is 1 plus 1 2 2 y plus k and this is minus 1 plus 1 0 1 y 1 Now on expanding along R3. We get our left-hand side is equal to This is equal to 3 y plus k into k into Into 1 into 2 y plus k Minus 2 y Spending along this is again equal to 3 y plus k Into k so this is equal to k square into 3 y plus k But this is our right-hand side our given determinant is equal to k square into 3 y plus k therefore left-hand side is Equal to right-hand side hence proved I Hope the question is clear to you by and enjoy yourself