AP EAMCET · Maths · Matrices
The rank of \(\left[\begin{array}{ccc}1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1\end{array}\right]\) is
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
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 .
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