TS EAMCET · Maths · Matrices
\(A\) is a singular matrix of order five. \(B\) is another matrix having the \(\operatorname{rank} \rho(B)\) equal to the rank \(\rho(A)\) and \(B\) has a non-zero minor of order 3. Then which one of the following is true?
- A \(B\) is a \(4 \times 4\) matrix
- B \(\rho(A)=\rho(B)=4\), irrespective of the order of \(B\)
- C \(\rho(A)=\rho(B)=3\), when all the fourth order minors of \(A\) are zero
- D \(|B|=0\)
Answer & Solution
Correct Answer
(C) \(\rho(A)=\rho(B)=3\), when all the fourth order minors of \(A\) are zero
Step-by-step Solution
Detailed explanation
Given that, Rank of matrix \(A=\) rank of matrix \(B\) \(f(A)=f(B) \text { and } f(B)=3\) \(\therefore\) Order of matrix \(B \geq\) Rank of matrix \(B\).
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