You're right, the problems should say:
1. Construct a 4-dimensional column matrix having the value i as it's ith component.
2. Construct a 5-dimensional row matrix having the value as it's jth component.
One problem says "Construct a 4-dimensional column matrix having the value j as its jth component." The answer in the book shows a 4 x 1 matrix with elements 1, 2, 3, 4. Shouldn't it be the value i as its ith component?
The problem right after that says "Construct a 5-dimensional row matrix having the value i^2 as its ith component." The answer in the book shows a 1 x 5 matrix with elements 1, 4, 9, 16, 25. Shouldn't it be the value of j as its jth component?
What do you see as the difference between j and i? Saying either "the value j as its jth component" or "the value i as its ith component" means simply that the 1st component is 1, the 2nd component is 2, the third component is 3rd component is 3, and the 4th component is 4. It doesn't matter if you use i or j.
Oh, it's starting to dawn on me. You have seen examples of m by n matrices where the rows were indexed by i and the columns by j. That is NOT a hard and fast rule. It doesn't matter what letter you use to index rows or columns as long as you are consistent. In these cases there is only one column or one row so there should be no ambiguity.The problem right after that says "Construct a 5-dimensional row matrix having the value i^2 as its ith component." The answer in the book shows a 1 x 5 matrix with elements 1, 4, 9, 16, 25. Shouldn't it be the value of j as its jth component?