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Let S be the set of all column matrices ...

Let S be the set of all column matrices `[(b_(1)),(b_(2)),(b_(3))]` such that `b_(1), b_(2), b_(2) in R` and the system of equations (in real variables)
`-x+2y+5z=b_(1)`
`2x-4y+3z=b_(2)`
`x-2y+2z=b_(3)`
has at least one solution. The, which of the following system (s) (in real variables) has (have) at least one solution for each `[(b_(1)),(b_(2)),(b_(3))] in S` ?

A

`x+2y+3z=b_1, 4y+5z=b_2` and `x+2y+6z=b_3`

B

`x+y+3z=b_1, 5x+2y+6z=b_2` and `-2x-y-3z=b_3`

C

`-x+2y-5z=b_1, 2x-4y+10z=b_2` and `x-2y+5z=b_3`

D

`x+2y+5z=b_1, 2x+3z=b_2` and `x+4y-5z=b_3`

Text Solution

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The correct Answer is:
A, D
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