Let T: R^2 --> R^2 be the linear operator given by the formula T(x,y) = (2x-y, -8x+4y)
Which of the following vectors are in R(T)?
a) (1, -4)
b) (5,0)
c) (-3, 12)
Which of the following vectors are in R(T)?
a) (1, -4)
b) (5,0)
c) (-3, 12)
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I will assume R(T) means the range of T.
Note that T(x,y) = (2x-y, -4(2x-y))
Therefore a) and c) are in range of T, but not b);
Note that T(x,y) = (2x-y, -4(2x-y))
Therefore a) and c) are in range of T, but not b);
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a and c