Suppose matrices are represented as lists of lists, as in the 3-by-4 case: [ [11, 12, 13, 14],

[21, 22, 23, 24],

[31, 32, 33, 34] ]

The car operator can be used to get the first row of such a matrix: (car [ [11, 12, 13, 14],

[21, 22, 23, 24],

[31, 32, 33, 34] ] )

will return the list [11, 12, 13, 14].

Similarly, cdr can be used to get the remaining rows after the first.

But, what if we want to extract the first column, made up of the first element of each row. A combination of map and car can be used for this purpose:

( map ( car [ [11, 12, 13, 14], [21, 22, 23, 24],

[31, 32, 33, 34] ] ) )

will return the list [11, 21, 31]. Here car is applied to each of the three lists corresponding to the three rows of the matrix. From each row, car extracts the first element, so the overall effect is to extract the first column.

Similarly, the remaining columns after the first can be extracted using a combination of map and cdr:

( map ( cdr [ [11, 12, 13, 14], [21, 22, 23, 24],

[31, 32, 33, 34] ] ) )

will return the list [ [12, 13, 14], [22, 23, 24], [32, 33, 34] ] .

Use this representation where matrices are represented as lists of lists, to implement the following operations on matrices. Write, execute, and thoroughly test your Dr. Racket recursive functions.

(a) Add corresponding elements of two matrices.