Given A 3 2 1 6 85 7 9 10 B 6 9 4 7 5 3 8 2 1 C 7 5 2 10 6

Given A = [3 -2 1 6 8-5 7 9 10]; B = [6 9 -4 7 5 3 -8 2 1]; C= [-7 -5 2 10 6 1 3 -9 8]; Find the following A+B+C Verify the associative law (A-B)+C=A+ (B-C) D=Transpose(AB) E=A^4 + B^2 - C^3 Find F, given that F = E^-1 * D^-1 - (A^T)^-1

Solution

a)=>
A+B+C = 2 2 -1
23 19 -1
2 2 19


b)=>
A+B = 9 7 -3
13 13 -2
-1 11 11

(A+B)+C = 2 2 -1
23 19 -1
2 2 19

B+C = -1 4 -2
17 11 4
-5 -7 9

A+(B+C)= 2 2 -1
23 19 -1
2 2 19
  
Hence (A+B)+C = A+(B+C)

c)=>

AB= 18-14-8 27-10+2 -12-6+1 -4 19 -17
36+56+40 54+40-10 -24+24-5 = 132 84 -5
42+63-80 63+45+20 -28+27+10 25 128 9
  
Transpose AB = -4 132 25
19 84 128
-17 -5 9
  
Hence D = -4 132 25
19 84 128
-17 -5 9
  
d)=>

A^4 = 2948   3261 2610
-11839 -12786   -5083
14158 8327 -5253
     
B^2 = 131   91   -1
53   94   -10
-42   -60   39
     
C^3 = -174   -76   -27
-79   -409   235
-618   -960   173
     
A^4+B^2-C3 = 3253 3428 2636
-11707 -12283 -5328
1 4734 9227 -5387

Hence E = 3253 3428 2636
-11707 -12283 -5328
14734 9227 -5387


e)=>

Transpose A = 3 6 7
-2 8 9
1 -5 10

Inverse of Transpose of A is = 125/563 -65/563 -2/563
29/563 23/563 -41/563
2/563 21/563 36/563