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Example A LINEAR TRANSFORMATION
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the matrix for a linear transformation from R2
into R2
The NULL SPACE of M
The RANGE of M
points on the line y x
points on the line y -2x
DOMAIN R2
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the matrix for a linear transformation from R2
into R2
The NULL SPACE of M
The RANGE of M
points on the line y x
points on the line y -2x
DOMAIN R2
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the matrix for a linear transformation from R2
into R2
The NULL SPACE of M
The RANGE of M
points on the line y x
points on the line y -2x
DOMAIN R2
Every point on the line y x 3 is mapped to
(-3,6)
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the matrix for a linear transformation from R2
into R2
The NULL SPACE of M
The RANGE of M
points on the line y x
points on the line y -2x
DOMAIN R2
Every point on the line y x - 4 is mapped to
(4,-8)
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the matrix for a linear transformation from R2
into R2
The NULL SPACE of M
The RANGE of M
points on the line y x
points on the line y -2x
The cosets of the null space are parallel lines
that partition the domain.
DOMAIN R2
Each of these lines is mapped to a single point
in the range.