question archive (4) 9a

(4) 9a

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(4) 9a. 11001 12 + 110112 = (leave your sum in base 2.) b. A4716 + B7916 = (leave your sum in base 16.) (10) 10. Suppose that A, B, and C are matrices of numbers. A has 5 rows and 4 columns, B has 4 rows and 6 columns. and C has 6 rows and 8 columns. Is it more efficient to compute the product as (AB)C or A(BC)? Justify your answer by computing the number of multiplications needed for each product. Number of Multiplications for (AB)C: Number of Multiplications for A(BC): Between (AB)C and A(BC), which is more efficient? (15) 11. Find a matrix A such that Put your A matrix here 4 2 A A= -3 -10

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a. 110011 + 11011

 = 01001110

b. A47 + B79 = 15C0

 

10. Multiplications for (AB)C = 5*4*6 + 5*6*8 = 120 + 240 = 360(first AB then C)

Multiplications for A(BC) = 4*6*8 + 5*4*8 = 192 + 160 = 352 (first BC then A)

 

Hence (AB)C is more efficient.

 

Given AB = C

A = CB-1

 

B-1 

1/10 -1/5
3/10 2/5

 

 

CB-1 =

 

1 2
-3 -4

Step-by-step explanation

a. 110011 + 11011

 = 01001110

b. A47 + B79 = 15C0

 

10. Multiplications for (AB)C = 5*4*6 + 5*6*8 = 120 + 240 = 360(first AB then C)

Multiplications for A(BC) = 4*6*8 + 5*4*8 = 192 + 160 = 352 (first BC then A)

 

Hence (AB)C is more efficient.

 

Given AB = C

A = CB-1

 

B-1 

1/10 -1/5
3/10 2/5

 

 

CB-1 =

 

1 2
-3 -4