4. Find the vector form of the general solution of the linear system х, + 2х — хз + 3x, 3D 4 X1 – 3x2 + x3 – 2x4 = -3 2x1 + 2x2 + x3 – x4 = 4 Hence find the following (i) Basis and dimension for the Null space of the coefficient matrix (ii) Basis and dimension for the Row space of the coefficient matrix

4. Find the vector form of the general solution of the linear system х, + 2х — хз + 3x, 3D 4 X1 – 3x2 + x3 – 2x4 = -3 2x1 + 2x2 + x3 – x4 = 4 Hence find the following (i) Basis and dimension for the Null space of the coefficient matrix (ii) Basis and dimension for the Row space of the coefficient matrix

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

4. Find the vector form of the general solution of the linear system
X1 + 2x2 – x3 + 3x4 = 4
X1 – 3x2 + x3 – 2x4 = -3
2x1 + 2x2 + x3 – x4 = 4
Hence find the following
(i) Basis and dimension for the Null space of the coefficient matrix
(ii) Basis and dimension for the Row space of the coefficient matrix
(iii) Rank of the coefficient matrix.

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