Let A be a 5 times 7 matrix, B be a 7 times 2 matrix, and C be a 2 times 3 matri

Question

Let A be a 5 times 7 matrix, B be a 7 times 2 matrix, and C be a 2 times 3 matrix. What is the size of ABC? How many operations (additions plus multiplications) does it take to compute AB? How many operations (additions plus multiplications) does it take to compute BC? How many operations (additions plus multiplications) does it take to compute ABC by first computing AB and then multiplying the result by C? How many operations (additions plus multiplications) does it take to compute ABC by first computing BC and then multiplying the result by A?

Explanation / Answer

(a)A=5*7 B=7*2 C=2*3

hence the size of ABC would be 5*3.

(b) A has 5 rows. And B has 2 columns.

For one row number and one column of multiplications = 7*7
For one row number and one column of multiplications = 7
Hence for 5 rows and one column = 5*(7^2+7)
And for 5 rows and 2 columns = 5*(7^2+7)*2 = 560

(c) Similarly for BC
Number of operations = 7*(2^2+2)*3= 126

(d) In the Computation of ABC by first calculating AB steps required = Operations rqd in computation of AB+Operations rqd in computation of ABC
= 560+ 5*(2^2+2)*3 =650

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