Find the value of x, if

Engineering

Mathematics

Introduction to Determinants

Question

∣ \begin{array}{cc} x + 2 & x \\ x - 4 & x + 3 \end{array} ∣ = ∣ \begin{array}{cc} 4 & 2 \\ - 2 & 5 \end{array} ∣

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∣ \begin{array}{cc} x + 2 & x \\ x - 4 & x + 3 \end{array} ∣ = ∣ \begin{array}{cc} 4 & 2 \\ - 2 & 5 \end{array} ∣

Since both have the same order, we can eqaute the corresponding rows and columns respectively.

x + 2 = 4 ⇒ x = 4 – 2 = 2

x = 2

⇒ x – 4 = – 2 ⇒ x = – 2 + 4 = 2

⇒ x + 3 = 5 ⇒ x = 5 – 3 = 2

∴ x = 2

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