Solved: Let A be an n n matrix and x Rn. (a) A scalar c can also be considered as a 1 1

Chapter 1, Problem 19

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Let A be an n n matrix and x Rn. (a) A scalar c can also be considered as a 1 1 matrix C = (c), and a vector b 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

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