Test Index

NDA Math Determinants

Question : 19 of 68

Marks: +1, -0

i^{\text{th}}

row and the

j^{\text{th}}

column of a determinant of third order is equal to

2(i+j)

. What is the value of the determinant?

[NDA-I 2021]

Validate

Solution: 👈: Video Solution

Concept

If all the elements of a row or column are zeroes, then the value of the determinant is zero. To evaluate the determinant row or column operation is done.

Calculation:

The determinant can be written as,

\begin{bmatrix} 2(1+1) & 2(1+2) & 2(1+3) \\ 2(2+1) & 2(2+2) & 2(2+3) \\ 2(3+1) & 2(3+2) & 2(3+3) \end{bmatrix}

= 2 \times \begin{bmatrix} 1+1 & 1+2 & 1+3 \\ 2+1 & 2+2 & 2+3 \\ 2+1 & 3+2 & 3+3 \end{bmatrix}

R_3 \rightarrow R_3 - R_1 \text{ and } R_2 \rightarrow R_2 - R_1

= 2 \times \begin{bmatrix} 1+1 & 1+2 & 1+3 \\ 1 & 1 & 1 \\ 2 & 2 & 2 \end{bmatrix}

R_3 \rightarrow R_3 - 2R_2

= 2 \times \begin{bmatrix} 1+1 & 1+2 & 1+3 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \end{bmatrix}

= 0

So, the value of the determinant is 0

Go to Question:

Prev Question

Next Question