the vectors X1111t and X2101t span the same plane as Y1424t

the vectors X1=[1,-1,1]^t and X2=[1,0,1]^t span the same plane as Y1=[4,-2,4]^t and Y2=[0,-1,0]^t. true or false? explain

Solution

True

(Y1-2Y2)/4=X2

(Y1+2Y2)/4=X1

Hence, X1,X2 belong to span of Y1,Y2

Hence, Span{X1,X2} is subset of span{Y1,Y2}

2X1+2X2=Y1

X1-X2=Y2

Hence, Y1,Y2 belong to span{X1,X2}

Hence, span{Y1,Y2} subset of span{X1,X2}

HEnce, span{X1,X2}=span{Y1,Y2}