7. Consider the transformation TR4 R4 defined by T(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4) (a) Find the associated matrix for T. (b) Find a basis for ker(T). (c) Find a basis for R(T) (Range). (d) Is T one-to-one? Why? (e) Is T onto? Why?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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7. Consider the transformation TR4 R4 defined by
T(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4)
(a) Find the associated matrix for T.
(b) Find a basis for ker(T).
(c) Find a basis for R(T) (Range).
(d) Is T one-to-one? Why?
(e) Is T onto? Why?
Transcribed Image Text:7. Consider the transformation TR4 R4 defined by T(x1, x2, x3, x4) = (x1, x1 + x2, x1 + x2 + x3, x1 + x2 + x3 + x4) (a) Find the associated matrix for T. (b) Find a basis for ker(T). (c) Find a basis for R(T) (Range). (d) Is T one-to-one? Why? (e) Is T onto? Why?
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