Write the value of the determinant |(2, 3, 4)(2x, 3x, 4x)(5, 6, 8)|.

Question

Write the value of the determinant \(\begin{vmatrix} 2 & 3 & 4 \\ 2x & 3x & 4x \\ 5 & 6 & 8 \end{vmatrix}.\)

Answer 1

Using the property that if the equimultiples of corresponding elements of other rows (or columns) are added to every element of any row (or column) of a determinant, then the value of determinant remains the same

Using row transformation, R₂ → R₂- x R₁

Using the property that if all elements of any row or column of a determinant are 0, then the value of determinant is 0.

Since R₂ has all elements 0, therefore ∆ = 0.