In: Advanced Math
Can ?⃑⃑ = ( 11 −5 9 ) be written as a linear combination of the vectors ?⃑ 1⃑ = ( 1 0 1 ), ?⃑⃑2⃑ = ( −2 3 −2 ), and ?⃑⃑3⃑ = ( −6 7 5 )? Does your answer allow you to conclude whether or not ? = {?⃑ 1⃑, ?⃑⃑2⃑, ?⃑⃑3⃑} is a basis for ? 3 ?
Create a vector ?⃑ such that the set {( 1 0 0 ) , ( 1 3 2 ) , ?⃑} is a basis for ? 3 . Explain.
ANSWER BOTH PARTS WILL RATE