JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Matrices

More JEE Advanced questions on Matrices

1. Which one of the following matrices can be obtained by performing elementary row transformations on the $3\times 3$ identity matrix ?
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2. Consider the matrix
   

   $$\mathrm{M}=\left[\begin{array}{cc}2& -1\\ 1& 0\end{array}\right]$$

   
   Let $\mathrm{p},\mathrm{q},\mathrm{r},\mathrm{s},\mathrm{a},\mathrm{b},\mathrm{c}$ and d be integers such that …
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3. Let $\mathbb{R}$ denote the set of all real numbers and let $\mathrm{i}=\sqrt{-1}$. Consider the matrices
   $\mathrm{S}=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ and $\mathrm{T}=\left[\begin{array}{ll}1& 1\\ 0& 1\end{array}\right]$.
   Let …
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4. Consider the matrix
   

   $$P=\left(\begin{array}{lll}2& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right).$$

   
   Let the transpose of a matrix $X$ be denoted by ${\mathrm{X}}^T$. Then the number of 3 × 3 invertible matrices Q with integer entries, such that …
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5. Let $I=\left(\begin{array}{ll}1& 0\\ 0& 1\end{array}\right)$ and $P=\left(\begin{array}{ll}2& 0\\ 0& 3\end{array}\right)$. Let $Q=\left(\begin{array}{ll}\mathrm{x}& \mathrm{y}\\ \mathrm{z}& 4\end{array}\right)$ for some non-zero real numbers $x,y$, and $z$, fo …
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6. Let $\alpha$ and $\beta$ be the distinct roots of the equation ${\mathrm{x}}^2+\mathrm{x}-1=0$. Consider the set $\mathrm{T}=\{1,\alpha ,\beta \}$. For a $3\times 3$ matrix $\mathrm{M}={\left({\mathrm{a}}_{\mathrm{ij}}\right)}_{3\times 3}$, define …
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