Let A = [aij] be a matrix of order 3 3, with aij = ( 2)i+j. If the sum of all the elements in the third row of A2 is + 2, , Z, then + is equal to :
(3) 224
aij=( 2)i( 2)j ⇒ A=uuT, u=( 2, 2, 2 2)T
A2=u(uTu)uT=14A (uTu=2+4+8)
Row 3 of A: 4, 4 2, 8 ⇒ sum =12+4 2
Row 3 of A2: 14(12+4 2)=168+56 2
∴ + =224
Answer: (3)
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