CBSE Class 12 · 2005 · MatricesLong Answer

More board questions on Matrices

1. The product of matrix $P$ and $Q$ is equal to a diagonal matrix. If the order of matrix $Q$ is $3\times 2$, then order of matrix $P$ is:
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2. If inverse of matrix $\left[\begin{array}{ccc}7& -3& -3\\ -1& 1& 0\\ -1& 0& 1\end{array}\right]$ is the matrix $\left[\begin{array}{lll}1& 3& 3\\ 1& \lambda & 3\\ 1& 3& 4\end{array}\right]$, then value of $\lambda$ is:
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3. Find the matrix $A^2$, where $A=[a_{ij}]$ is a $2\times 2$ matrix whose elements are given by $a_{ij}=\max (i,j)-\min (i,j)$:
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4. If $A$ is a square matrix of order $3$ such that the value of $|\mathrm{adj}A|=8$, then the value of $|A^{\top }|$ is:
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5. If $A=\left[\begin{array}{ccc}1& 2& -3\\ 2& 3& 2\\ 3& -3& -4\end{array}\right]$, then find $A^{-1}$ and hence solve the following system of equations:
   

   $$x+2y-3z=-4,2x+3y+2z=2,3x-3y-4z=11.$$
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6. If $A$ is a $2\times 3$ matrix such that $AB$ and $A{B}^{\prime }$ both are defined, then order of matrix $B$ is:
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