Given a matrix transformation [ <mtable rowspacing="4pt" columnspacing="1em"> <mtr

ownerweneuf

ownerweneuf

Answered question

2022-05-23

Given a matrix transformation [ 0 1 0 0 ] , why does it go from R 2 to R 2 , when it squishes the plane into a line?

Answer & Explanation

Hugo Bruce

Hugo Bruce

Beginner2022-05-24Added 10 answers

The image of the point ( a , b ) is
f ( a , b ) = ( 0 a + 1. b , 0 a + 0 b ) = ( b , 0 )
all images are in the line whose equation is y = 0.
f is from R 2 to R 2 but f ( R 2 ) = { ( x , 0 ) : x R } is a line.
f is not surjective.

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