5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3, -9,-3, 6), y = (2, 5, 1, -4), 8 = (-2, –4,0, 4). %3D (a) Which conditions must the real numbers a, b, c, d satisfy in order the vector (a, b, c, d) belongs to W. (b) Find a basis A for W. What is dim W ? (c) If (5,8,-2,-10) E W find the coordinate matrix of (5, 8, -2,-10) relative to the basis A.

5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3, -9,-3, 6), y = (2, 5, 1, -4), 8 = (-2, –4,0, 4). %3D (a) Which conditions must the real numbers a, b, c, d satisfy in order the vector (a, b, c, d) belongs to W. (b) Find a basis A for W. What is dim W ? (c) If (5,8,-2,-10) E W find the coordinate matrix of (5, 8, -2,-10) relative to the basis A.

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

5. Let W be the subspace of the vector space V = R' spanned by the vectors
a = (1,3, 1, -2), B = (-3, -9,-3,6), y (2,5, 1,-4), 8 = (-2, -4,0, 4).
%3D
(a) Which conditions must the real numbers a, b, c, d satisfy in order the
vector (a, b, c, d) belongs to W.
(b) Find a basis A for W. What is dim W ?
(c) If (5,8, –2,-10) € W find the coordinate matrix of (5, 8, -2, –10)
relative to the basis A.

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