Determinants Matrices Question 63
Question: What is the value of the determinant $ \begin{vmatrix} 1 & bc & a(b+c) \\ 1 & ca & b(c+a) \\ 1 & ab & c(a+b) \\ \end{vmatrix}- $
Options:
A) $ 0 $
B) $ abc $
C) $ ab+bc+ca $
D) $ abc(a+b+c) $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ \begin{vmatrix} 1 & bc & a(b+c) \\ 1 & ac & b(c+a) \\ 1 & ab & c(a+b) \\ \end{vmatrix} $
Applying $ C_3\to C_2+C_3 $
$ \begin{vmatrix} 1 & bc & ab+bc+ac \\ 1 & ac & ab+bc+ac \\ 1 & ab & ab+bc+ac \\ \end{vmatrix} $
$ =(ab+bc+ac) \begin{vmatrix} 1 & bc & 1 \\ 1 & ac & 1 \\ 1 & ab & 1 \\ \end{vmatrix} $
$ =(ab+bc+ac)\times 0=0 $
BETA
