A homogeneous system of equations is a system of the formX1a11a12ainx2Am2Amn..ат1(b) Prove that a homogeneous system has a nontrivial solution if and only if the system hasat least one free variable.

Given: A homogeneous system of equations is a11a12..a1n..........am1am2..amnx1x2..xn=00..0

Answered: A homogeneous system of equations is a…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.5: Cramer's Rule

Problem 35PS

See similar textbooks

Similar questions

If a system of linear equations has infinitely many solutions, then the system is called _____ . If a system of linear equations has no solution, then the system called ____.
If a system of linear equations has infinitely many solutions, then the system is called _______. If a system of linear equations has no solutions, then the system is called ______.
Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.
Solve the homogeneous linear system corresponding to the coefficient matrix. [121200242412]
Suppose a nonhomogeneous system of nine linear equations in ten unknowns has a solution for all possible constants on the right sides of the equations. Is it possible to find two nonzero solutions of the associated homogeneous system that are not multiples of each other? Discuss.
Determine the values of α such that the linear system has: (i) unique solution (ii) nosolution (iii) infinitely many solution: into row-echelon form:
Is it possible for a nonhomogeneous system of seven equations in six unknowns to have a unique solution for some right-hand side of constants? Is it possible for such a system to have a unique solution for every right-hand side? Explain.

Recommended textbooks for you

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

A homogeneous system of equations is a system of the form a11 a12 din X2 Amn Aml Am2 Xn (b) Prove that a homogeneous system has a nontrivial solution if and only if the system has at least one free variable.