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2023 PEA Q16

A=(101011110). A=\begin{pmatrix}1&0&1\\ 0&1&1\\ 1&1&0\end{pmatrix}.

Rank of AA?

The available source text does not include a full option block for this item, so the question is marked needsReview.
Reveal answer and solution

Answer

A

Solution

  1. 1

    det⁡A=1(1⋅0−1⋅1)−0+1(0⋅1−1⋅1)=−1−1=−2≠0\det A=1(1\cdot 0-1\cdot 1)-0+1(0\cdot 1-1\cdot 1)=-1-1=-2\ne 0. So rank =3=3.

Answer structure / marking notes

Needs review: source TeX does not provide a full four-option MCQ block.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2023/ISI_MSQE_PEA_2023_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.