Test Index

NDA Math Determinants

Question : 13 of 68

Marks: +1, -0

\Delta

is the value of the determinant

\begin{vmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{vmatrix}

then what is the value of the following determinant?

\begin{vmatrix} pa_{1} & b_{1} & qc_{1} \\ pa_{2} & b_{2} & qc_{2} \\ pa_{3} & b_{3} & qc_{3} \end{vmatrix}

(p \neq 0 \; \text{ or } \; 1, q \neq 0 \; \text{ or } \; 1)

[NDA-I 2021]

$p \Delta$
$q \Delta$
$(p+q) \Delta$
pq $\Delta$

Validate

Solution: 👈: Video Solution

Concept:

Using Scalar Multiple Property:

If all the elements of a row (or column) of a determinant are multiplied by a non-zero constant, then the determinant gets multiplied by the same constant.

Calculation:

\Delta = \begin{vmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{vmatrix}

Column 1 of all elements is multiplied by

p

then given matrices is also multiplied by

p

Again column 3 of all elements is multiplied by q then given matrices is also multiplied by

q

pq \Delta = \begin{vmatrix} pa_{1} & b_{1} & qc_{1} \\ pa_{2} & b_{2} & qc_{2} \\ pa_{3} & b_{3} & q c_{3} \end{vmatrix}

Go to Question:

Prev Question

Next Question