Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Given that the value of a determinant of order three is zero; which one of the following is not correct? 

Options:

The elements of any two rows are proportional

The elements of any two coloumns are proportional

The elements of the diagonal are all non-zero and all other elements are zero

The elements of second row are average of elements of first and second row

Correct Answer:

The elements of the diagonal are all non-zero and all other elements are zero

Explanation:

In part 3

Let say we have a matrix with non zero diagonal elements and all other zero elements

in this case 

e.g.  A3×3 = $\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right]$

then |A| = abc ≠ 0

so option 3