Telegram group: T.me/BBCNOUN [MTH212] Let \(T:\ U\ \to \ V\) be defined by T(u) = 0 for all \(u\ \in \ U\). Then T is a _____ transformation zero [MTH212] Let U and V be vector spaces over a field F, and let \(T:U\to\ V\) be a one-one and onto linear transformation. The T is called Isomorphism [MTH212] Consider the function \(T:R^{2}\to\ R^{2}:\) \(T\left(x,y\right)=\ \left(x,-y\right)\) is _________ reflection [MTH212] Let~\(T:R^{2}\to R^{2}\)~be the transformation~ \(T\left(x_{1},x_{2}\right)=\left(x_{1},0\right)\).The null space (or kernel)~~of~\(T\)~is \(\left(0,x_{2}\right)\) [MTH212] Let \(T:\ U\ \to\ V\) be defined by T(u) = u for all \(u\ \in\ U\).Then T is a ______ transformation Identity [MTH212] Let \(F:R^{4}\to R^{3}\) defined by \(F\left(x,y,z,t\right)=\left(x-y+z+t,\ x+2z-t,\ x+y+3z-3t\right).\ \)Find \(F(0,0,0,1)\) (1,-1,-3) [MTH212] Consider the function \(p:R^{3}\to\ R^{2}:\) \(p\left(x,y,z\right)=\ \left(x,y\right)\) is a ______ from \(R^{3}\) on to the xy-plane projection [MTH212] Let \(L:R^{3}\to\ R\) be the map given by \(L(x,y,z)\ =\ x\ +\ y\ +\ z\). What is nullity (L)? 2 [MTH212] Consider the linear transformation defined by \(F\left(x,y,z\right)=\left(yz,x^{2}\right).\ \)Find\(F(2,3,4)\) (12,4) [MTH212] Let \(F:R^{3}\to\ R^{2}\) and \(G:R^{3}\to\ R^{2}\) be defined by \(F\left(x,y,z\right)=\left(2x,y+z\right)\) and \(F\left(x,y,z\right)=\left(x-z,y\right)\), determine F +G \(\left(3x-z,2y+z\right)\)