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MHT CET202522 Apr 2025Evening ShiftMathematicsMatricesActual

If matrix A= 1 11 [ array rrr -1 & 7 & -24 2 & a & 4 2 & -3 & 15 array ] and A⁻¹= [ array rrr 3 & 3 & 4 2 & -3 & 4 b & -1 & c array ] , then the values of a, b, c respectively are ......

Options

  1. A3,1,0
  2. B-6 11 , 0, 1 11
  3. C-3,0,1
  4. D-3 11 , 0, 1 11

Correct answer

C. -3,0,1

Step-by-step solution

Given the matrices: A = 1 11 bmatrix -1 & 7 & -24 2 & a & 4 2 & -3 & 15 bmatrix A⁻¹ = bmatrix 3 & 3 & 4 2 & -3 & 4 b & -1 & c bmatrix Since A A⁻¹ = I , we compute the product without the scalar factor first: bmatrix -1 & 7 & -24 2 & a & 4 2 & -3 & 15 bmatrix bmatrix 3 & 3 & 4 2 & -3 & 4 b & -1 & c bmatrix = 11I Determine b from the (1,1) entry: (-1)(3) + (7)(2) + (-24)(b) = 11 -3 + 14 - 24b = 11 -24b = 0 b = 0 Determine a from the (2,2) entry: (2)(3) + (a)(-3) + (4)(-1) = 11 6 - 3a - 4 = 11 -3a = 9 a = -3 Determine

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