If then x =

Engineering

Mathematics

Introduction to Determinants

Properties of Determinant

Question

If $∣ \begin{array}{ccc} 1 & 0 & 0 \\ 2 & 3 & 4 \\ 5 & - 6 & x \end{array} ∣ = 45$ then x =

– 5

– 7

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Given $∣ \begin{array}{ccc} 1 & 0 & 0 \\ 2 & 3 & 4 \\ 5 & - 6 & x \end{array} ∣ = 45$
By operation of matrix (5),
1(3x + 24) = 45
3x = 21
⇒ x = 7