R". (b) Determine the composite linear transformation TL and find its rank and nullity.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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answer letter b only
4. Let L: R?
and let T : R³
→ R³ be the linear transformation given by L(x1, x2)
→ R³ be the linear transformation given by T(y1, Y2, Y3) = (-y1+ Y3, Yı +
(x1 + x2, -X1 + x2, X1)
%3D
Y2, -Y1 + 2y3).
(a) Determine the matrix representation of L and T with respect to the standard bases for
R".
(b) Determine the composite linear transformation TL and find its rank and nullity.
Transcribed Image Text:4. Let L: R? and let T : R³ → R³ be the linear transformation given by L(x1, x2) → R³ be the linear transformation given by T(y1, Y2, Y3) = (-y1+ Y3, Yı + (x1 + x2, -X1 + x2, X1) %3D Y2, -Y1 + 2y3). (a) Determine the matrix representation of L and T with respect to the standard bases for R". (b) Determine the composite linear transformation TL and find its rank and nullity.
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