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COMEDK2024Evening ShiftMathematicsMatricesActual

If the matrix A is such that A ( array cc -1 & 2 3 & 1 array )= ( array cc -4 & 1 7 & 7 array ) then A is equal to

Options

  1. A( array cc 1 & -1 2 & 3 array )
  2. B( array cc 1 & 1 2 & -3 array )
  3. C( array cc -1 & 1 2 & 3 array )
  4. D( array cc 1 & 1 -2 & 3 array )

Correct answer

A. ( array cc 1 & -1 2 & 3 array )

Step-by-step solution

Let A = pmatrix a & b c & d pmatrix and B = pmatrix -1 & 2 3 & 1 pmatrix . The given equation is AB = C , where C = pmatrix -4 & 1 7 & 7 pmatrix . To find A , we compute A = CB⁻¹ . First, find the determinant of B : |B| = (-1)(1) - (2)(3) = -1 - 6 = -7 . The inverse of B is given by B⁻¹ = 1 |B| adj (B) = 1 -7 pmatrix 1 & -2 -3 & -1 pmatrix = pmatrix -1/7 & 2/7 3/7 & 1/7 pmatrix . Now, calculate A = CB⁻¹ = pmatrix -4 & 1 7 & 7 pmatrix pmatrix -1/7 & 2/7 3/7 & 1/7 pmatrix . The first row of A is: a₁₁ = (-4)(-1/7) + (

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