i. Determine whether the set is linearly dependent or linearly independent. S = {(-2,1,3), (2,9, –3), (2,3, –3)}

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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i. Determine whether the set is linearly dependent or linearly independent.
S= {(-2,1,3), (2,9, –3), (2,3, –3)}
ii. Determine whether S is a basis for P3.
S = {1– 2x? + x³, -4 + x²,2x + x³, 5x}
iii. Find the nullity of the linear Transformation T.
T: Ps → P2,rank (T) = 3
iv. Find the kernel of the Linear Transformation T.
T:R? → R², T(x,y) = (x – y,y – x)
Transcribed Image Text:i. Determine whether the set is linearly dependent or linearly independent. S= {(-2,1,3), (2,9, –3), (2,3, –3)} ii. Determine whether S is a basis for P3. S = {1– 2x? + x³, -4 + x²,2x + x³, 5x} iii. Find the nullity of the linear Transformation T. T: Ps → P2,rank (T) = 3 iv. Find the kernel of the Linear Transformation T. T:R? → R², T(x,y) = (x – y,y – x)
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