‹ Back to the paper
Choose the correct option.
2 |x y z; p q r; a b c| + |x y z; s t u; 2a 2b 2c| Which one of the following is equal to the above…
$2 \begin{vmatrix} x & y & z \\ p & q & r \\ a & b & c \end{vmatrix} + \begin{vmatrix} x & y & z \\ s & t & u \\ 2a & 2b & 2c \end{vmatrix}$
Which one of the following is equal to the above sum?
- (a)$\begin{vmatrix} 3x & 3y & 3z \\ 2p+s & 2q+t & 2r+u \\ 4a & 4b & 4c \end{vmatrix}$
- (b)$\begin{vmatrix} 2x & 2y & 2z \\ 2p+s & 2q+t & 2r+u \\ 2a & 2b & 2c \end{vmatrix}$
- (c)$\begin{vmatrix} x & y & z \\ p+s & q+t & r+u \\ 2a & 2b & 2c \end{vmatrix}$
- (d)$\begin{vmatrix} 2x & 2y & 2z \\ p+s & q+t & r+u \\ 4a & 4b & 4c \end{vmatrix}$
Answer
Answer
Correct option: (c)
Answer: (c) the determinant with rows $(x, y, z)$, $(p+s, q+t, r+u)$, $(2a, 2b, 2c)$
Taking the factor 2 into the third row, $2\begin{vmatrix} x & y & z \\ p & q & r \\ a & b & c \end{vmatrix} = \begin{vmatrix} x & y & z \\ p & q & r \\ 2a & 2b & 2c \end{vmatrix}$. Two determinants that differ only in the second row add by adding those rows.