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Let A= ( array lll 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 array ) . If u₁ and u₂ are column matrices such that A u₁= ( array l 1 0 0 array ) and A u₂= ( array l 0 1 0 array ) , then u₁+u₂ is equal to

Options

  1. A( array c -1 1 0 array )
  2. B( array c -1 1 -1 array )
  3. C( array c -1 -1 0 array )
  4. D( array c 1 -1 -1 array )

Correct answer

D. ( array c 1 -1 -1 array )

Step-by-step solution

A= ( array lll 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 array ) Let u₁= [ array l a b c array ] ; u₂= [ array l d e f array ] Au ₁= [ array l 1 0 0 array ] u₁= [ array c 1 -2 1 array ] Au ₂= [ array l 0 1 0 array ] u ₂= [ array c 0 1 -2 array ] u ₁+ u ₂= [ array c 1 -1 -1 array ]

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