Let A be an n × n matrix and x ∈ Rn.
(a) A scalar c can also be considered as a l × l matrix C = (c), and a vector be ∈ Rn can be considered as an n × 1 matrix B. Although the matrix multiplication CB is not defined, show that the matrix product BC is equal to cb, the scalar multiplication of c times b.
(b) Partition A into columns and x into rows and perform the block multiplication of A times x.
(c) Show that
Ax = x1a1 + x2a2 + ... + xnan