 Hi, welcome to the session. I am Deepika here. Let's discuss the question. Construct a 3 by 4 matrix whose elements are given by aij is equal to half mod of minus 3i plus j. Let us first understand the definition of mod x. Mod x is defined as mod x is equal to x if x is greater than equal to 0 and it is equal to minus x if x is strictly less than 0. This is the key idea behind this question. Let's start the solution. In general, our 3 by 4 matrix is given by a is equal to a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34. Now aij is equal to half mod of minus 3i plus j. Now for a11 we will put i is equal to 1 and j is equal to 1. So a11 is equal to half minus 3 into 1 plus 1 which is equal to half into minus 2 mod of minus 2 which is equal to half into 2 which is equal to 1. Now a12 is equal to half mod of minus 3 into 1 plus 2 which is equal to half of minus 1 which is equal to 1 by 2. a13 is equal to half mod of minus 3 into 1 plus 3 which is equal to half mod of 0 which is again equal to 0. a14 is equal to half mod of minus 3 into 1 plus 4 which is equal to half into mod of 1 which is equal to half. Now, a21 is equal to half, mod of minus 3 into 2 plus 1, which is equal to half, mod of minus 5, which is equal to half into 5, that is equal to 5 by 2. For a22, we have half, mod of minus 3 into 2 plus 2, which is equal to half, mod of minus 4, which is equal to half into 4, which is equal to 2. a23 is equal to half, mod of minus 3 into 2 plus 3, which is equal to half of mod minus 3, which is equal to half into 3, 3 by 2. Now, a24 is equal to half into minus 3 into 2 plus 4, which is equal to half into mod of minus 2, half into 2, that is equal to 1. a31 is equal to half, mod of minus 3 into 3 plus 1, which is equal to half minus 8, this is equal to half into 8, which is equal to 4. Now, a32 is equal to half, mod of minus 3 into 3 plus 2, which is equal to half minus 7, which is equal to 7 by 2. Now, a33 is equal to half minus 3 into 3 plus 3, which is equal to half minus 6, which is equal to half into 6, 3. Now, a34 is equal to half minus 3 into 3 plus 4, which is equal to half, mod of minus 5, which is equal to half into 5, that is equal to 5 by 2. Hence, the required matrix is given by is given by is equal to 1, 1 by 2, 0, 1 by 2, 5 by 2, 2, 3 by 2, 1, 4, 7 by 2, 3 and 5 by 2. This is our answer. I hope the question is clear to you. Bye and have a good day.