Make this ralupop!!
If α β × δ β = γ γ γ , find the trace of the following matrix:
A = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ α 8 8 7 5 8 1 0 0 2 8 9 β 3 5 3 2 1 2 5 4 6 2 5 7 3 γ 3 5 6 3 6 2 5 2 2 4 5 5 7 2 5 δ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤
Details and assumptions
α , β , γ and δ are digits, eg α β = α × β .
D o L i k e a n d s h a r e
The answer is 21.
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2 solutions
I guess there is more of number theory in this problem than algebra,..first..the hint to solve the problem lies in yyy.so all three digits are same.simple way is to note down all 9 such possible numbers starting from 111, 222 ...I e all the multiples of 111..till 999..once u have this figured out its easy.note that 111 has 2 prime factors.ie 3 and 37..so its obviously not the answer...so evidently from a fixed 2 digit number like 37, only job left is to see who the other guy is who ends with 7 and is obtained by multiplying 3 with an integer.so its 3x9=27..., split the digits as required to find a+b+c+d.=21
3 7 × 2 7 = 9 9 9
Trace of A = α + β + γ + δ
= 3 + 7 + 9 + 2 = 2 1