CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

What is the value of the determinant $$\begin{vmatrix} 1 & bc & a\left( b+c \right)  \\ 1 & ca & b\left( c+a \right)  \\ 1 & ab & c\left( a+b \right)  \end{vmatrix}$$?


A
0
loader
B
abc
loader
C
ab+bc+ca
loader
D
abc(a+b+c)
loader

Solution

The correct option is A $$0$$
Now, in the matrix
$$\begin{vmatrix} 1 & bc & ab+ac \\ 1 & ac & bc+ba \\ 1 & ab & ca+cb \end{vmatrix}$$

$$C_3\rightarrow C_3+C_2$$

$$ \begin{vmatrix} 1 & bc & ab+ac+bc \\ 1 & ac & ab+ac+bc \\ 1 & ab & ab+ac+bc \end{vmatrix}$$    taking $$(ab+bc+ac)$$ common in $$C_3$$

$$(ab+bc+ac)$$$$ \begin{vmatrix} 1 & bc & 1 \\ 1 & ac & 1 \\ 1 & ab & 1 \end{vmatrix}$$
Now two columns of the matrix are same so it's determinant will be 0.
(a)

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image