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Recall the vector space P(3) consisting of all polynomials in the variable z of degree at most 3. Consider the following collections, X, Y, Z, of elements of P(3). X:= {0, 2-1, x² + 3, z³}, Y :={1, x + 4, (x − 2) - (x + 2), 3 - x³}, Z := {x³ + x² + x + 1, x² + 1, x + 1, x, 1, 0}. In each case decide if the statement is true or false. (i) span(X) = P(3). (No answer given) (ii) span(Z) = P(3). (No answer given)

Recall the vector space P(3) consisting of all polynomials in the variable z of degree at most 3. Consider the following collections, X, Y, Z, of elements of P(3). X:= {0, 2-1, x² + 3, z³}, Y :={1, x + 4, (x − 2) - (x + 2), 3 - x³}, Z := {x³ + x² + x + 1, x² + 1, x + 1, x, 1, 0}. In each case decide if the statement is true or false. (i) span(X) = P(3). (No answer given) (ii) span(Z) = P(3). (No answer given)

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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Recall the vector space P(3) consisting of all polynomials in the variable z of degree at most 3. Consider the following collections, X, Y, Z, of elements of P(3). X: {0, 2.x, x² + 3, x³}, Y :={1, x + 4, (x − 2) - (x + 2), 3 - x³}, Z :={x³ + x² + x + 1, x² + 1, x + 1, x, 1, 0}. In each case decide if the statement is true or false. (i) span(X) = P(3). (No answer given) (ii) span(Z) = P(3). (No answer given) (iii) Y is a basis for P(3). (iv) Z is a basis for P(3). (No answer given) (No answer given)
Transcribed Image Text:Recall the vector space P(3) consisting of all polynomials in the variable z of degree at most 3. Consider the following collections, X, Y, Z, of elements of P(3). X: {0, 2.x, x² + 3, x³}, Y :={1, x + 4, (x − 2) - (x + 2), 3 - x³}, Z :={x³ + x² + x + 1, x² + 1, x + 1, x, 1, 0}. In each case decide if the statement is true or false. (i) span(X) = P(3). (No answer given) (ii) span(Z) = P(3). (No answer given) (iii) Y is a basis for P(3). (iv) Z is a basis for P(3). (No answer given) (No answer given)
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