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Find the inverse functions

Find the inverse (begin{pmatrix} 5 & 3 \ 6 & 4 end{pmatrix})

  • A.
    (begin{vmatrix} 2 & -frac{3}{2} \ -3 & -frac{5}{2} end{vmatrix})
  • B.
    (begin{vmatrix} 2 & -frac{3}{2} \ -3 & frac{5}{2} end{vmatrix})
  • C.
    (begin{vmatrix} 2 & frac{3}{2} \ -3 & frac{5}{2} end{vmatrix})
  • D.
    (begin{vmatrix} 2 & frac{3}{2} \ -3 & frac{5}{2} end{vmatrix})
Correct Answer: Option B
Explanation

Let A = (begin{pmatrix} 5 & 3 \ 6 & 4 end{pmatrix})
Then |A| = (begin{pmatrix} 5 & 3 \ 6 & 4 end{pmatrix}) = 20 – 18 = 2
Hence A-1 = (frac{1}{|A|}begin{pmatrix} 4 & -3 \ -6 & 5 end{pmatrix})
= (frac{1}{2}begin{pmatrix} 4 & -3 \ -6 & 5 end{pmatrix})
= (begin{pmatrix} 4 times 1/2 & -3 times 1/2 \ -6 times 1/2 & 5 times 1/2 end{pmatrix})
= (begin{pmatrix} 2 & -frac{3}{2} \ -3 & frac{5}{2} end{pmatrix})