Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

$\left|\begin{array}{ccc} a+b & a+2 b & a+3 b \\ a+2 b & a+3 b & a+4 b \\ a+4 b & a+5 b & a+6 b \end{array}\right|=$

Options:

$a^2+b^2+c^2-3 a b c$

3ab

3a + 5b

0

Correct Answer:

0

Explanation:

$\left|\begin{array}{ccc}a+b & a+2 b & a+3 b \\ a+2 b & a+3 b & a+4 b \\ a+4 b & a+5 b & a+6 b\end{array}\right|=\left|\begin{array}{ccc}a+b & a+2 b & a+3 b \\ b & b & b \\ 3 b & 3 b & 3 b\end{array}\right|=0$

by applying R2 → R2 – R1

R3 → R3 – R1

Hence (4) is the correct answer.