I need help with a linear algebra problem computing operations. Let A be a 5 tim

Question

I need help with a linear algebra problem computing operations.

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

1)

A is 5x7 B is 7x2 and C is 2x3

if A=IxJ and B =MxN then AB is possible if J=M and its size = IxN

size of AB =5x2

and size of (AB) C = 5x3

2)

A contains 7 column and 5 row

and B contains 7 row and 2 column

we konw that in multipication row of matrix one is multipied by column of matrix two

so in each element of AB matrix computed by 7 times multipication and 6 times addition = toatal 13 operation is required to compute one element

also size of AB will be 5X2 . Hence it contained total 5*2 =10 element

Hence total operation required is 10*13=130

3)

C contains 3 column and 2 row

and B contains 7 row and 2 column

we konw that in multipication row of matrix one is multipied by column of matrix two

so in each element of BC matrix computed by 2 times multipication and 1 times addition = toatal 3 operation is required to compute one element

also size of AB will be 7x3 . Hence it contained total 7*3 =21 element

Hence total operation required is 21*3=63

4)

We already computed AB which required 130 operation

now computation of each element of (AB) C required 2 multipication and 1 addition = 3 operation

and toatl element present in ABC is 5x3=15 hence 15*3 = 45 operations

total operation = 45+130= 175

e) now we already computed BC whose size is 7x3 and it required 63 operation

NOW each element of A (BC) can be computed by 7 multiplication and 6 additition = 13 operation

total element in A(BC) = 5*3=15 hence 15*13=195 operation

Total opertaion = 195+63= 258

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.