Need some help in Linear Algebra Cramers rule. Thanks in advance Consider the system3x1 + 2x2 – x3 = 1-2x1 + ax2 + x3 = 2Xi + x2 = 31. Find the values of a for which this system has a unique solution, then useCramer's rule to find the explicit solution, potentially as a function of a.2. For all values of a for which the system doesn't have a unique solution,use Gaussian elimination to find out if the system has infinite solutionsor no solution. If the system has infinite solutions, find an expression forthem

1)If it has a unique solution, then the determinant of the coefficient matrix doesn’t vanish.…

Answered: Consider the system 3x1 + 2x2 – x3 = 1…

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

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Need some help in Linear Algebra Cramers rule. Thanks in advance

Consider the system
3x1 + 2x2 – x3 = 1
-2x1 + ax2 + x3 = 2
Xi + x2 = 3
1. Find the values of a for which this system has a unique solution, then use
Cramer's rule to find the explicit solution, potentially as a function of a.
2. For all values of a for which the system doesn't have a unique solution,
use Gaussian elimination to find out if the system has infinite solutions
or no solution. If the system has infinite solutions, find an expression for
them

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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