Solution-Write down a description of the range

Write down a description of the range

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Reference no: EM13275985

(1) Consider the linear transformation T : R⁴ -> R³ dened by T(x, y, z, w) = (x + 2y z + w; x 2y + z 2w; x + 2y z):

(a) By directly using the denition of the range of a linear transformation, write down a description of the range R(T); and determine a nonzero vector in it.

(b) Find description of R(T) as the intersection of hyperplanes and deduce a basis for R(T) and the rank r(T):

(d) Verify the the theorem T : V ! W, then dim(V ) = r(T)+n(T) for the linear transformation considered above

Reference no: EM13275985

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Write down a description of the range

Reference no: EM13275985

Reference no: EM13275985

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