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Let T:R5 → R4 be a linear transformation defined by T(x)= Ax where x in R5 and A= 2 1 3 1 0 0-2 0 1 -1 0 0 0 2 8 a. Find a basis for the range of T b. Find the rank of T, nullity of T and also verify whether T is 1-1, onto. Justify your answer.

Let T:R5 → R4 be a linear transformation defined by T(x)= Ax where x in R5 and A= 2 1 3 1 0 0-2 0 1 -1 0 0 0 2 8 a. Find a basis for the range of T b. Find the rank of T, nullity of T and also verify whether T is 1-1, onto. Justify your answer.

Advanced Engineering Mathematics
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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77557 Let A= R³ R4 be a linear transformation defined by T(x)= Ax where x in R5 and 8 12 0 1-1 2 1 3 10 0 1 -1 0-2 000 28 a. Find a basis for the range of T b. Find the rank of T, nullity of T and also verify whether T is 1-1, onto. Justify your answer.
Transcribed Image Text:77557 Let A= R³ R4 be a linear transformation defined by T(x)= Ax where x in R5 and 8 12 0 1-1 2 1 3 10 0 1 -1 0-2 000 28 a. Find a basis for the range of T b. Find the rank of T, nullity of T and also verify whether T is 1-1, onto. Justify your answer.
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