Recognize and appropriately apply subscripts in 1, 2, and 3 dimensions.

1. Correctly convert from variables to subscripted variables. For example, rewrite the repression 3x-(4y+7xz)/(2y-3x²) using subscripted variables in x.
   Web Content:
   • Palay: Subscripted Variables 6:34 (script).
   • Palay: Subscripted Variables Extended 5:26 (script).
2. Correctly expand a given term of a sequence described using a formula involving subscripted variables. For example, given the sequence x_i=3i+5 find the 7th term of the sequence.
   Web Content:
   • Palay: Subscripts in Expressions 8:05 (script).
   • Palay: Subscripts in Expressions - Page 2 4:02 (script).
3. Given the formula for a row of Pascal's triangle, correctly produce a specified row of the triangle. For example, produce the eighth row (it starts with 1 7) of Pascal's Triangle.
   Web Content:
   • Palay: Subscripts and Pascal 13:05 (script).
4. Correctly identify 2-dimensional matrix elements specified by subscript. For example, in a given matrix (say it is 5x5) what is the value of the element (2,3)?
   Web Content:
   • Khan Academy: introduction-to-the-matrix 4:29
   • Khan Academy: matrix_dimensions worksheet
   • Palay: Matrix Elements 4:56 (script).
5. Correctly fill a nxm matrix given a rule for matrix elements that determines their value from their subscripts. For example, write out a 3x4 matrix where the (i,j) element of the matrix is given by 2i-3j.
   Web Content:
   • Palay: Filling a Matrix via a Rule 3:36 (script).
6. Correctly convert a given mxn matrix, held in column major order, to a list of values. For example, convert the following column-major ordered matrix to an ordered list.
   Web Content:
   • Palay: Matrix to List 2:41 (script).
7. Correctly identify 3-dimensional matrix elements specified by subscript. For example, in a given matrix (say it is 5x5x5) what is the value of the element (2,4,3)?
   Web Content:
   • Palay: Three Dimensional Arrays 4:14 (script).
8. Given a 3-dimensional matrix of values, correctly create a 2-dimensional sub-matrix by taking a specified slice of the matrix. For example, given the following 4x5x3 matrix, form a 2-dimensional matrix representing the slice created by holding the second dimension constant at 3.
   Web Content:
   • Palay: Slices of a Three Dimensional Matrix (Array) 5:45 (script).