Exercise 2.37.  Suppose we represent vectors v = (vi) as sequences of 
numbers, and matrices m = (mij) as sequences of vectors (the rows of the 
matrix). For example, the matrix

 [ 1 2 3 4 ]
 | 4 5 6 6 |
 [ 6 7 8 9 ]

is represented as the sequence ((1 2 3 4) (4 5 6 6) (6 7 8 9)). With 
this representation, we can use sequence operations to concisely express 
the basic matrix and vector operations. These operations (which are 
described in any book on matrix algebra) are the following:

(dot-product v w)        returns the sum ∑ᵢ vᵢwᵢ.

(matrix-*-vector m v)    returns the vector t, where tᵢ = ∑ⱼ mᵢⱼvⱼ.

(matrix-*-matrix m n)    returns the matrix p, where pᵢⱼ = ∑ᵣ mᵢᵣvᵣⱼ.

(transpose m)            returns the matrix n, where nᵢⱼ = mⱼᵢ

We can define the dot product as:

(define (dot-product v w)
  (accumulate + 0 (map * v w)))

Fill in the missing expressions in the following procedures for 
computing the other matrix operations. (The procedure accumulate-n is 
defined in exercise 2.36.)

(define (matrix-*-vector m v)
  (map <??> m))
(define (transpose mat)
  (accumulate-n <??> <??> mat))
(define (matrix-*-matrix m n)
  (let ((cols (transpose n)))
    (map <??> m)))

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(define (matrix-*-vector m v)
  (map (lambda (row) (dot-product row v)) m))

(define (transpose m)
  (accumulate-n cons nil m))

(define (matrix-*-matrix m n)
  (let ((cols (transpose n)))
    (map (lambda (row) (matrix-*-vector cols row)) m)))