Question

(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 \( x \).

Answer 1

(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