(Solved): 1.6 Vector of differences. Suppose \( x \) is an \( n \)-vector. The associated vector of differen ...

1.6 Vector of differences. Suppose \( x \) is an \( n \)-vector. The associated vector of differences is the \( (n-1) \)-vector \( d \) given by \( d=\left(x_{2}-x_{1}, x_{3}-x_{2}, \ldots, x_{n}-x_{n-1}\right) \). Express \( d \) in terms of \( x \) using vector operations (e.g., slicing notation, sum, difference, linear combinations, inner product). The difference vector has a simple interpretation when \( x \) represents a time series. For example, if \( x \) gives the daily value of some quantity, \( d \) gives the day-to-day changes in the quantity.