Draw the cuts in A (2 by 3) and B (3 by 4) and AB to show how each of the four multiplication rules is really a block multiplication:(1) Matrix A times columns of B.    Columns of AB(2) Rows of A times the matrix B.    Rows of AB(3) Rows of A times columns of B.  Inner products (numbers in AB)(4) Columns of A times rows of B.  Outer products (matrices add to AB)

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Draw the cuts in A (2 by 3) and B (3 by 4) and AB to show how each of the four multiplication rules is really a block multiplication:
(1) Matrix A times columns of B.    Columns of AB
(2) Rows of A times the matrix B.    Rows of AB
(3) Rows of A times columns of B.  Inner products (numbers in AB)
(4) Columns of A times rows of B.  Outer products (matrices add to AB)

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