JEE Main · 2008 · 27 Apr 2008 · Offline · Matrices

More JEE Main questions on Matrices

1. For some $\alpha ,\beta \in R$, let $A=\left[\begin{array}{ll}\alpha & 2\\ 1& 2\end{array}\right]$ and $B=\left[\begin{array}{ll}1& 1\\ 1& \beta \end{array}\right]$ be such that $A^2-4A+2I=B^2-3B+I=O$. Then …
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2. For the matrices $\mathrm{A}=\left[\begin{array}{cc}3& -4\\ 1& -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}-29& 49\\ -13& 18\end{array}\right]$, if …
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3. If the system of equations
   $3\mathrm{x}+\mathrm{y}+4\mathrm{z}=3$
   $2\mathrm{x}+\alpha \mathrm{y}-\mathrm{z}=-3$
   $\mathrm{x}+2\mathrm{y}+\mathrm{z}=4$
   has no solution, then the value of $\alpha$ is equal to:
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4. If $\mathrm{A}=\left[\begin{array}{ll}2& 3\\ 3& 5\end{array}\right]$, then the determinant of the matrix $({\mathrm{A}}^{2025}-3{\mathrm{A}}^{2024}+{\mathrm{A}}^{2023})$ is
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5. Let A be a $3\times 3$ matrix such that $\mathrm{A}+{\mathrm{A}}^{\mathrm{T}}=\mathrm{O}$. If …
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6. If $X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$ is a solution of the system of equations $AX=B$, where $\text{adj }A=\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& 5\\ 1& -2& 3\end{array}\right]$ and $B=\left[\begin{array}{c}4\\ 0\\ 2\end{array}\right]$, then $|x+y+z|$ is equal t …
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