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(i) If \( x \in N \) and \( \left|\begin{array}{ll}x & 3 \\ 4 & x\end{array}\right|=\left|\begin{array}{rr}4 & -3 \\ 0 & 1\end{array}\right| \), find the value(s) of \( x \)(ii) If \( x \in I \) and \( \left|\begin{array}{cc}2 x & 3 \\ -1 & x\end{array}\right|=\left|\begin{array}{ll}3 & 1 \\ x & 3\end{array}\right| \), find the value(s) of \( x \). |
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Answer» (i) \(\begin{vmatrix}x&3\\4&3\end{vmatrix}\) = \(\begin{vmatrix}4&-3\\0&1\end{vmatrix}\) ⇒ x2 - 12 = 4 ⇒ x2 = 16 ⇒ x = -4 or x = 4. (ii) \(\begin{vmatrix}2x&3\\-1&x\end{vmatrix}\) = \(\begin{vmatrix}3&1\\x&3\end{vmatrix}\) ⇒ 2x2 + 3 = 9 - x ⇒ 2x2 + x - 6 = 0 ⇒ 2x2 + 4x - 3x - 6 = 0 ⇒ (2x - 3) (x + 2) = 0 ⇒ x = 3/2 or -2 |
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