Q23.Consider the statements: P: V=R2 with addition (x1,y1)+(x2,y2)=(x1x2,y1y2) and scalar multiplication c(x,y)=(cx,cy) is a vector space. Q: Let V be a vector space. If u,v,w∈V are such that au+bv+cw=0 for some scalars a,b,c∈R and ac=0, then span{u,v}=span{v,w}. Statement 1: P is true, but Q is false. Statement 2: Q is true, but P is false. Statement 3: Both P and Q are true. Statement 4: Both P and Q are false. Which statement is correct? Enter its serial number.
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Q23
16 Oct 2022
Q23.Consider the statements: P: V=R2 with addition (x1,y1)+(x2,y2)=(x1x2,y1y2) and scalar multiplication c(x,y)=(cx,cy) is a vector space. Q: Let V be a vector space. If u,v,w∈V are such that au+bv+cw=0 for some scalars a,b,c∈R and ac=0, then span{u,v}=span{v,w}. Statement 1: P is true, but Q is false. Statement 2: Q is true, but P is false. Statement 3: Both P and Q are true. Statement 4: Both P and Q are false. Which statement is correct? Enter its serial number.
