Let fi = 1+a + 5r², f2 = 1+ 2x + 8r². B = (f1, f2) is a basisfor the subspaceV = {ao+a,x+ aza² : 2a0 + 3a1 – az = 0}of R2[r].()Let g = -3+4r + 6x². If [g]Bthen s =%3Da) 10b) 3c) -3d) -10e) vector g is not in V.

s = - 10 (option a) The detailed solution is as follows below:

Let fi = 1+a + 5a², f2 = 1 + 2x + 8a². B = (f1, f2) is a basis for the subspace V = {ao +a;# + azw² : 2ao + 3a, – az = 0} of Ra[r]. () Let g = -3+ 4æ + 6a². If [g]8 then s= %3D a) 10 b) 3 c) -3 d) -10 e) vector g is not in V.

Let fi = 1+a + 5a², f2 = 1 + 2x + 8a². B = (f1, f2) is a basis for the subspace V = {ao +a;# + azw² : 2ao + 3a, – az = 0} of Ra[r]. () Let g = -3+ 4æ + 6a². If [g]8 then s= %3D a) 10 b) 3 c) -3 d) -10 e) vector g is not in V.

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let fi = 1+a + 5r², f2 = 1+ 2x + 8r². B = (f1, f2) is a basis
for the subspace
V = {ao+a,x+ aza² : 2a0 + 3a1 – az = 0}
of R2[r].
()
Let g = -3+4r + 6x². If [g]B
then s =
%3D
a) 10
b) 3
c) -3
d) -10
e) vector g is not in V.

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