#### need solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 19

Hint: Here, we use basic concept of determinant of matrix

Given:

\begin{aligned} &b_{i 1}=2 a_{i 1} \\ &b_{i 2}=3 a_{i 2} \\ &b_{i 3}=4 a_{i 3} i, i=1,2,3 \end{aligned}

Let $\left | A \right |=\left [ a_{ij} \right ]$ and $B=b_{ij}$ be a square matrix of order 3 and $\left | A \right |=5$

Solution:

\begin{aligned} &|B|=\left(\begin{array}{lll} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{array}\right) \\ &|B|=\left(\begin{array}{lll} 2 a_{11} & 3 a_{12} & 4 a_{13} \\ 2 a_{21} & 3 a_{22} & 4 a_{23} \\ 2 a_{31} & 3 a_{32} & 4 a_{33} \end{array}\right) \end{aligned}

Let’s transfer $\left | B \right |=\left | B^{T} \right |$ So,

\begin{aligned} &|B|=\left(\begin{array}{ccc} 2 a_{11} & 2 a_{12} & 2 a_{13} \\ 3 a_{21} & 3 a_{22} & 3 a_{23} \\ 4 a_{31} & 4 a_{32} & 4 a_{33} \end{array}\right) \\ &|B|=2 \times 3 \times 4\left(\begin{array}{lll} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array}\right) \end{aligned}

\begin{aligned} &=24 \times\left|A^{T}\right| \\ &=24 \times 5 \quad\left[|A|=\left|A^{T}\right|=5\right] \\ &=120 \end{aligned}