logo

Ask Questions, Get Answers

X
 
Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Matrices

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

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

1 Answer

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
 

Related questions

Download clay6 mobile appDownload clay6 mobile app
...
X