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
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
If \(\Delta=\left|\begin{array}{lll} {a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}} \end{array}\right|\) and Aij is Cofactors of aij, then the value of \(\Delta\) is given by
Using the property of determinant and without expanding prove that \(\left| {\begin{array}{*{20}{c}} 0&a&{ - b} \\ { - a}&0&{ - c} \\ b&c&0 \end{array}} \right| = 0\)