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If \(\left|\begin{array}{cc} {x} & {2} \\ {18} & {x} \end{array}\right|=\left|\begin{array}{cc} {6} & {2} \\ {18} & {6} \end{array}\right|\) , then x is equal to
  • \(\pm\)6
  • 0
  • -6
  • 6
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If \(\left|\begin{array}{cc} {x} & {2} \\ {18} & {x} \end{array}\right|=\left|\begin{array}{cc} {6} & {2} \\ {18} & {6} \end{array}\right|\) , then x is equal to
  • \(\pm\)6
  • 0
  • -6
  • 6

Answer

We have \(\left|\begin{array}{ll} {x} & {2} \\ {18} & {x} \end{array}\right|=\left|\begin{array}{ll} {6} & {2} \\ {18} & {6} \end{array}\right|\)
We know that determinant of A is calculated as \(|A|=\left|\begin{array}{ll} {a} & {b} \\ {c} & {d} \end{array}\right|\) = ad - bc
\(\Rightarrow\) x(x) – 2(18) = 6(6) – 2(18)
\(\Rightarrow\) x2 - 36 = 36 – 36
\(\Rightarrow\) x2 =36 – 36 + 36
\(\Rightarrow\) x2 = 36
\(\Rightarrow\) x = \(\pm\)6
Therefore the choice is: A
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