(25 points overall) Consider the linear map f R (3) R (3) given by ( x , y , z ) ( x 2y 3z , 2x y 3z , 3x y 2z ) Do the following (a) (10 points) Determine dimension of ker(f) and a basis for it Is f one to one or not (b) (10 points) Determine dimension of im(f) and a basis for it Is f onto or not (c) (10 points) Check if the vector v ( 1 , 1 , 1 ) is in the image of f or not 1 (25 points overall) Consider the linear map f R3R3 given by xyzx 2y 3z2x y 3z3xy 2z Do the following (a) (10 points) Determine dimension of ker(f) and a basis for it Is f one to one or not (b) (10 points) Determine dimension of im(f) and a basis for it Is f onto or not (c) (10 points) Check if the vector v 111 is in the image of f or not

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Question: (25 points overall) Consider the linear map f:R^(3)->R^(3) given by ([x],[y],[z])|->([x+2y+3z],[2x+y+3z],[3x-y+2z]) Do the following: (a) (10 points) Determine dimension of ker(f) and a basis

(25 points overall) Consider the linear map

f:R^(3)->R^(3)

given by\

([x],[y],[z])|->([x+2y+3z],[2x+y+3z],[3x-y+2z])

\ Do the following:\ (a) (10 points) Determine dimension of

ker(f)

and a basis for it. Is

f

one-to-one or not?\ (b) (10 points) Determine dimension of

im(f)

and a basis for it. Is

f

onto or not?\ (c) (10 points) Check if the vector\

v=([1],[1],[1])

\ is in the image of

f

or not.

$(25 points overall) Consider the linear map f:R^(3)->R^(3) given by\ ([x],[y],[z])|->([x+2y+3z],[2x+y+3z],[3x-y+2z])\$

1. (25 points overall) Consider the linear map f:R3R3 given by xyzx+2y+3z2x+y+3z3xy+2z Do the following: (a) (10 points) Determine dimension of ker(f) and a basis for it. Is f one-to-one or not? (b) (10 points) Determine dimension of im(f) and a basis for it. Is f onto or not? (c) (10 points) Check if the vector v=111 is in the image of f or not

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