Determinants Matrices Question 164
Question: The determinant is equal to
Options:
A) $ \begin{vmatrix} bx+ay & cx+by \\ b’x+a’y & c’x+b’y \\ \end{vmatrix} $
B) $ \begin{vmatrix} ax+by & bx+cy \\ a’x+b’y & b’x+c’y \\ \end{vmatrix} $
C) $ \begin{vmatrix} bx+cy & ax+by \\ b’x+c’y & a’x+b’y \\ \end{vmatrix} $
D) $ \begin{vmatrix} ax+by & bx+cy \\ a’x+b’y & b’x+c’y \\ \end{vmatrix} $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ Let\Delta = \begin{vmatrix} y^{2} & -xy & x^{2} \\ a & b & c \\ a’ & b’ & c’ \\ \end{vmatrix} $ Then, [Applying $ C_1\to xC_1,C_3\to yC_3 $ ] [Applying $ C_1\to C_1+yC_2,C_3\to C_3+xC_2 $ ] [Expanding along $ R_1 $ ]
BETA
