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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
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 |