Q22.If addition and scalar multiplication on V=R2 are defined as follows: addition: (x1,y1)+(x2,y2)=(0,0) for (x1,y1),(x2,y2)∈V; scalar multiplication: c(x,y)=(0,0) for (x,y)∈V and c∈R. Consider the statements: 1. There exists an element 0 in V such that 0+v=v for all v∈V. 2. For each v∈V and a,b∈R, (a+b)v=av+bv. 3. For each scalar a∈R and v1,v2∈V, a(v1+v2)=av1+av2. 4. For each v∈V and a,b∈R, (ab)v=a(bv). Which statement is not true? Enter the serial number.
Save
Check
Details
Q22
16 Oct 2022
Q22.If addition and scalar multiplication on V=R2 are defined as follows: addition: (x1,y1)+(x2,y2)=(0,0) for (x1,y1),(x2,y2)∈V; scalar multiplication: c(x,y)=(0,0) for (x,y)∈V and c∈R. Consider the statements: 1. There exists an element 0 in V such that 0+v=v for all v∈V. 2. For each v∈V and a,b∈R, (a+b)v=av+bv. 3. For each scalar a∈R and v1,v2∈V, a(v1+v2)=av1+av2. 4. For each v∈V and a,b∈R, (ab)v=a(bv). Which statement is not true? Enter the serial number.
