ExamBro
ExamBro
TS EAMCET · Maths · Matrices

The rank of \(\left[\begin{array}{ccc}1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1\end{array}\right]\) is

  1. A \(0\)
  2. B \(1\)
  3. C \(2\)
  4. D \(3\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(3\)

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & \text { Let } A=\left[\begin{array}{ccc} 1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1 \end{array}\right] \\ & \therefore \quad|A|=1(1+1)+1(1-1)+1(1+1) \\ & =4 \neq 0 \\ & \end{aligned} \] \(\therefore\) Rank of matrix \(A\) is 3 .