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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Matrices
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The number of $3\times 3$ matrices A whose entries are either 0 or 1 and for which the system $A=\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\0\\0\end{bmatrix}$ has exactly two distinct solution is

$(a)\;0\qquad(b)\;2^9-1\qquad(c)\;168\qquad(d)\;2$

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1 Answer

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Let $A=\begin{bmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{bmatrix}$
Where $a_i,b_i,c_i$ have values 0 or 1 for $i$=1,2,3
Then the given system is equivalent to
$a_1x+b_1y+c_1z=1$
$a_2x+b_2y+c_2z=0$
$a_3x+b_3y+c_3z=0$
Which represent three distinct planes .But three planes cannot intersect at two distinct points therefore no such system exists.
Hence (a) is the correct answer.
answered Nov 20, 2013 by sreemathi.v
 

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