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Yukti Vault

Matrices - JEE Mathematics question (JEE Advanced 2009 Paper 1)

Comprehension · Questions 1–1

Read the passage given below and answer the questions that follow.

Let $\mathcal{A}$ be the set of all $3\times3$ symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.
JEE Advanced 2009 Paper 1Question 1
The number of matrices $A$ in $\mathcal{A}$ for which the system of linear equations $$A\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$$ is inconsistent, is
Matrices
Options for question 1, choose one

Solution

Inconsistent means $\operatorname{rank}A<\operatorname{rank}[A|b]$. Checking the $6$ singular matrices, exactly $4$ of them are inconsistent, which is more than $2$.

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