Give an example of a matrix B such that the linear transformation S: R3 to R4 defined by S(x)=Bx has the following property: R(S)={(x1,x2,x3,x4)/…

1. Give an example of a matrix B such that the linear transformation S: R3 to R4 defined by S(x)=Bx has the following property: R(S)={(x1,x2,x3,x4)/ x1+x2+x3+x4=0}

2. Give an example of a matrix C such that the linear transformation P: R3 to R4 defined by P(x)=Cx has the following property: Ker(P)=R3