Define T:R7 R5 byT([x1,x2,x3,x4,x5,x6,x7]) = [x1+x2+x5+x6,x1+x3+x4+x5+x6, x2 - x3 - x4 + x5 - x7, 2x1 + x2 + x3 + x4 + x5 + 2x6 + x7, x1 - x2 + 2x3...

1. Define T:R7 →R5 byT([x1,x2,x3,x4,x5,x6,x7]) = [x1+x2+x5+x6,x1+x3+x4+x5+x6, x2 – x3 – x4 + x5 – x7, 2x1 + x2 + x3 + x4 + x5 + 2x6 + x7, x1 – x2 + 2x3 + 2x4 – x5 + x6 + 2x7]. Find the matrix of T in the standard bases ({εj}). Find dim(ker(T)) and dim(Im(T)).

2, 3 Attached (A, B)