Let T : R6 → R2 be a linear operator such that T(x1, X2, X3, X4, X5, X6) (a) What is [T], the matrix of T? (b) What is the rank of [T]? (c) Give a basis for the range of T. = X1 + X₂2+X3 X4+X5+X6 3 3 >

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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7. Let T: R6 → R2 be a linear operator such that
x1 + x2 + x3 x4+x5+x6
(201₁-
3
3
T(x1, x2, x3, x4, X5, X6)
(a) What is [T], the matrix of T?
(b) What is the rank of [T]?
(c) Give a basis for the range of T.
=
2
Transcribed Image Text:7. Let T: R6 → R2 be a linear operator such that x1 + x2 + x3 x4+x5+x6 (201₁- 3 3 T(x1, x2, x3, x4, X5, X6) (a) What is [T], the matrix of T? (b) What is the rank of [T]? (c) Give a basis for the range of T. = 2
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