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###### Akash Jaiswal posted an Question
October 12, 2021 • 20:10 pm 30 points
• IIT JAM
• Mathematics (MA)

# Let a be a5 x3 real matrix of rank 2 . let b e r° be a non-zero vector that is in the column space of a. let s = {re r°: ar = b}. define the translation of a su

Let A be a5 x3 real matrix of rank 2 . Let b E R° be a non-zero vector that is in the column space of A. Let S = {rE R°: Ar = b}. Define the translation of a subspace V of R° by zo E R° as the set zo+ V= {ro +v:vEV}. Then (A) S is the empty set B) 5 has only one element C) Sis a translation of a l dimensional subspace D) Sis a translation of a 2 dimensional subspace

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• ##### Anonymous User Best Answer

since rank of A is 2 and is nonzero vector therefore rank of AB not equal to 2 rank of A ≠ rank of AB system AX=b is inconsistent.no x€R³ exist such that AX=b so S is empty option A

system inconsistent kaise

A ka rank 2 hai and b non zero to AB ka rank≠2 hoga

ye aise to system consistent h?

then s is infinite elements

mene (1 2 3 4 5)^T liye tha

if we take b =(1,1,1,0,0) then system inconsistent

check

question mai b non zero diya if we take (1,1,1,0,0) then system inconsistent and s is empty

aapne b=(1 1 1 0 0) kaise liya b to colomn vector h A ka par 11100 colom vector nhi h

(1,1,1,0,0)^T

check attachment

??

check

check attachment

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