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If 2 A+3 B= [ array ccc 2 & -1 & 4 3 & 2 & 5 array ] and A+2 B= [ array lll 5 & 0 & 3 1 & 6 & 2 array ] then B=

Options

  1. A[ array ccc 8 & -1 & 2 -1 & 10 & -1 array ]
  2. B[ array ccc -8 & -1 & -2 1 & -10 & 1 array ]
  3. C[ array ccc 8 & 1 & -2 -1 & 10 & -1 array ]
  4. D[ array ccc 8 & 1 & 2 -1 & 10 & -1 array ]

Correct answer

D. [ array ccc 8 & 1 & 2 -1 & 10 & -1 array ]

Step-by-step solution

Let M₁ = 2A + 3B = bmatrix 2 & -1 & 4 3 & 2 & 5 bmatrix and M₂ = A + 2B = bmatrix 5 & 0 & 3 1 & 6 & 2 bmatrix . We want to find B . Multiply the second equation by 2 : 2(A + 2B) = 2 bmatrix 5 & 0 & 3 1 & 6 & 2 bmatrix = bmatrix 10 & 0 & 6 2 & 12 & 4 bmatrix . Now subtract the first equation from this result: (2A + 4B) - (2A + 3B) = bmatrix 10 & 0 & 6 2 & 12 & 4 bmatrix - bmatrix 2 & -1 & 4 3 & 2 & 5 bmatrix . B = bmatrix 10-2 & 0-(-1) & 6-4 2-3 & 12-2 & 4-5 bmatrix = bmatrix 8 & 1 & 2 -1 & 10 & -1 bmatrix . Answer:

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