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The number of 3xx3 matrices A whose entr...

The number of `3xx3` matrices `A` whose entries are either `0or1` and for which the system `A[x y z]=[1 0 0]` has exactly two distinct solution is a. 0 b. `2^9-1` c. `168` d. `2`

A

0

B

`2^(9)-1`

C

168

D

2

Text Solution

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The correct Answer is:
A
Three planes cannot intersect at two distinct points.
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Knowledge Check

  • The number of 3xx3 matrices A whose entries are either 0 or 1 and tor which the system A[(x),(y),(z)]=[(1),(0),(0)] has exactly two distinct solutions is

    A
    0
    B
    `2^(9)-1`
    C
    168
    D
    2

  • The number of 3 xx 3 matrices A whose entries are either 0 or 1 and for which the system A[(x),(y),(z)]=[(1),(0),(0)] has exactly two distinct solutions is

    A
    Zero
    B
    One
    C
    Two
    D
    None of these

  • The number of 3xx3 matrices A whose entries are either 0 or 1 and for which the system of equations A [(x),(y),(z)]=[(2),(0),(3)] has exactly five distinct solution is

    A
    0
    B
    511
    C
    1024
    D
    5

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