Q25.If addition and scalar multiplication on V=R2 are defined by (x1,y1)+(x2,y2)=(x1+x2,y1+y2) and c(x,y)=(x,cy), consider the statements: 1. There exists a zero vector 0∈V such that 0+v=v for all v∈V. 2. There exists a vector v′∈V such that v′+v=v+v′=0 for all v∈V. 3. For each v∈V, 1v=v. 4. For each v∈V and a,b∈R, (a+b)v=av+bv. 5. For each a∈R and v1,v2∈V, a(v1+v2)=av1+av2. 6. For each v∈V and a,b∈R, (ab)v=a(bv). Which statement is not true? Enter the serial number.
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Q25
5 Jun 2022
Q25.If addition and scalar multiplication on V=R2 are defined by (x1,y1)+(x2,y2)=(x1+x2,y1+y2) and c(x,y)=(x,cy), consider the statements: 1. There exists a zero vector 0∈V such that 0+v=v for all v∈V. 2. There exists a vector v′∈V such that v′+v=v+v′=0 for all v∈V. 3. For each v∈V, 1v=v. 4. For each v∈V and a,b∈R, (a+b)v=av+bv. 5. For each a∈R and v1,v2∈V, a(v1+v2)=av1+av2. 6. For each v∈V and a,b∈R, (ab)v=a(bv). Which statement is not true? Enter the serial number.
