QUESTIONS - CDOG - VECTORS

QUESTIONS - ANSWERS - CDOG - VECTORS
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Let u=(-1,1,0,2). Determine whether u is orthogonal to the subspace spanned by the vectors w1=(0,0,0,0), w2=(1,-1,3,0), w3=(4,0,9,2).
WE HAVE TO SHOW THAT
U.[AW1+BW2+CW3]=0…. FOR ANY VALUE OF A,B AND C
IT WILL BE SO IF
U.W1=U.W2=U.W3=0
HERE WE HAVE
U.W1=-1*0+1*0+0*0+2*0=0…OK
U.W2=-1*1+1*-1+0*3+2*0=-2…..NOT ZERO HENCE NOT ORTHOGONAL

HENCE U IS NOT ORTHOGONAL TO THE SUBSPACE SPANNED BY …W1,W2,W3.