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Problem 24 : Let b b2 b3 ba E R4 be a fixed vector, b + 0. Define L:R4 R by C1 12 L(x) = b. I, 2= ER4. 13 24 where bºx is the

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Sodi. Dimension theorem: let voud w be vector space and Let LIV w be linear them nullity (it rand (1)= dim (v) Given L: RR LObia;= -b₂ X ₂ biz az-budy. 2) ?, = -0.1. bit be/6, 43. - but the Now na by dy bi 10+ 12 du bu _belb, balla 22 1 bulbi 0 So KeSo Rank (L) & Rad (4) This is onto: we know nullity (L) = din (kerl) کہا 3: An rank of L=1

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