Find a basis and the dimension of the solution space W of each of the following homogencous systems:+ 2y – 2z+ 2s - t= 0x+ 2y - z+ 3s – 21 = 02x + 4y – 7z+ s+ t= 0(b) x+ 2y - z+38 – 4t =02r + 4y – 2: - s+ St =02r + 4y – 2: +4s – 21 = 0(a)

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Find a basis and the dimensi on of the soluti on space W of each of the following homogeneous systems: (a) + 2y – 2:+ 2s – t= 0 x+ 2y - + 3s – 21 = 0 2x + 4y – 72+ s+ t=0 (b) x+ 2y - z+38 - 4t -0 2r + 4y – 2: - s+ 5t=0 2r + 4y – 2: +4s – 21 =0

Find a basis and the dimensi on of the soluti on space W of each of the following homogeneous systems: (a) + 2y – 2:+ 2s – t= 0 x+ 2y - + 3s – 21 = 0 2x + 4y – 72+ s+ t=0 (b) x+ 2y - z+38 - 4t -0 2r + 4y – 2: - s+ 5t=0 2r + 4y – 2: +4s – 21 =0

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

Find a basis and the dimension of the solution space W of each of the following homogencous systems:
+ 2y – 2z+ 2s - t= 0
x+ 2y - z+ 3s – 21 = 0
2x + 4y – 7z+ s+ t= 0
(b) x+ 2y - z+38 – 4t =0
2r + 4y – 2: - s+ St =0
2r + 4y – 2: +4s – 21 = 0
(a)

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