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If 3 A+4 B^t= ( array ccc 7 & -10 & 17 0 & 6 & 31 array ) and 2 B-3 A^t= ( array cc -1 & 18 4 & -6 -5 & -7 array ) then (5 B)^t=

Options

  1. A( array ccc 5 & 5 & 10 15 & 0 & 20 array )
  2. B( array ccc 5 & -5 & 10 15 & 0 & 20 array )
  3. C( array ccc 5 & -5 & -10 15 & 0 & -20 array )
  4. D( array ccc -5 & 5 & 10 -15 & 0 & 20 array )

Correct answer

B. ( array ccc 5 & -5 & 10 15 & 0 & 20 array )

Step-by-step solution

Given equations: 1) 3A + 4B^t = pmatrix 7 & -10 & 17 0 & 6 & 31 pmatrix 2) 2B - 3A^t = pmatrix -1 & 18 4 & -6 -5 & -7 pmatrix Taking the transpose of equation (2): (2B - 3A^t)^t = pmatrix -1 & 18 4 & -6 -5 & -7 pmatrix ^t 2B^t - 3A = pmatrix -1 & 4 & -5 18 & -6 & -7 pmatrix Now we have a system of equations in A and B^t : i) 3A + 4B^t = pmatrix 7 & -10 & 17 0 & 6 & 31 pmatrix ii) -3A + 2B^t = pmatrix -1 & 4 & -5 18 & -6 & -7 pmatrix Adding (i) and (ii): 6B^t = pmatrix 7-1 & -10+4 & 17-5 0+18 & 6-6 & 31-7 pmatrix =

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