Please provide explantaion to each
Are the following linear transformations? T::R2 rightarrowR3 defined by T(x, y)=pi2x, 0,y/2) T: R2rightarrowR3 defined by T(x, y)=(x+y, x-y, xy) T: R2rightarrowR3 defined by T(x, y)=(l,0,0) T: R2rightarrowR3 defined by T(x, y)=(y, x, y) T: R2rightarrowR3 defined by T(x, y)=(x, x2, x3) T: R2rightarrowR3 defined by T(x, y)=(2x+3y, 3x+4y, 4x+5y) T P rightarrow P defined by T(f(x))=f(0)+f'(0)x+f"(0)x2 T P P rightarrow P defined by T(f(x))=f(l)+f'(2)x+f"(3)x2 T P rightarrowP defined by T(f(x))=f(x-3) T P rightarrowP defined by T(f(x))=f(x)-3 f' denotes the derivative of f
Show transcribed image text Are the following linear transformations? T::R2 rightarrowR3 defined by T(x, y)=pi2x, 0,y/2) T: R2rightarrowR3 defined by T(x, y)=(x+y, x-y, xy) T: R2rightarrowR3 defined by T(x, y)=(l,0,0) T: R2rightarrowR3 defined by T(x, y)=(y, x, y) T: R2rightarrowR3 defined by T(x, y)=(x, x2, x3) T: R2rightarrowR3 defined by T(x, y)=(2x+3y, 3x+4y, 4x+5y) T P rightarrow P defined by T(f(x))=f(0)+f'(0)x+f"(0)x2 T P P rightarrow P defined by T(f(x))=f(l)+f'(2)x+f"(3)x2 T P rightarrowP defined by T(f(x))=f(x-3) T P rightarrowP defined by T(f(x))=f(x)-3 f' denotes the derivative of f