Consider the following linear equations are part of a homogeneous system; X3 – x, +2.x, + x, Зх, + 6х, +3х, — 3х, +2x, X +2x, + x, – X; 2x + 4х, — 2х, + 4х, — бх, — 5х, a) Find the rank of the matrix b) Find basic solutions and express the general solution as a linear combination of the basic solutions. (Please write your answer in the format given below: a) rank = x b) basic solutions are 1: [a b c d]; 2: [e f g h];

Consider the following linear equations are part of a homogeneous system; X3 – x, +2.x, + x, Зх, + 6х, +3х, — 3х, +2x, X +2x, + x, – X; 2x + 4х, — 2х, + 4х, — бх, — 5х, a) Find the rank of the matrix b) Find basic solutions and express the general solution as a linear combination of the basic solutions. (Please write your answer in the format given below: a) rank = x b) basic solutions are 1: [a b c d]; 2: [e f g h];

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

Consider the following linear equations are part of a homogeneous system;
X3 – x, + 2x, +Xg
3x, + 6х, +3х, — 3х, +2х,
x +2x, + x, – xs
2.x, + 4x, – 2x, +4x, – 6x, - 5x,
a) Find the rank of the matrix
b) Find basic solutions and express the general solution as a linear
combination of the basic solutions.
(Please write your answer in the format given below:
a) rank = x
b) basic solutions are
1: [a b c d];
2: [e fg h];

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