EBK ALGEBRA FOUNDATIONS
EBK ALGEBRA FOUNDATIONS
15th Edition
ISBN: 9780321978929
Author: Martin-Gay
Publisher: PEARSON
bartleby

Videos

Question
Book Icon
Chapter E, Problem 1ES
To determine

To solve:the givenset of linearequationfor value of variable using matrices and mathematical methodologies.

Expert Solution & Answer
Check Mark

Answer to Problem 1ES

The value of variable is x=2 and y=1 .

Explanation of Solution

Given information:

The given is below set of linear equation:

  {x+y=1x2y=4}

Calculation:

The given is below set of linear equation:

  {x+y=1x2y=4}

The given equation is re-written below in matrices form:

  {x+y=1x2y=4}( 1 1 1 2 )( x y )=( 1 4 )

This matrix representation is in form of:

  AX=B

Here matrix A represents coefficients of linear equation, matrix B represents the resultant of two equation and matrix X represents variables of linear equations. Applying matrix properties as below:

  AX=BA-1AX=A-1B [multiply both side byA-1]IX=A-1B [Iis identity matrix and IX=X ]X=A-1B

So, the value of variables of linear equation is equal to product of inverse of matrix A and matrix B.

Now it is known that inverse of matrix is equal to adjoint of A divided by determinant of matrix A, as below:

  A1=1|A|adj(A)

Put value in above formula to find value of A inverse for given linear equation:

  A1=1(1)(2)(1)(1)( 2 1 1 1 )A1=121( 2 1 1 1 )A1=13( 2 1 1 1 )

Put value A inverse and B in formula for variables, as below:

  X=A-1B( x y )=13( 2 1 1 1 )( 1 4 )( x y )=13( 6 3 ) [multiply the matrices first]( x y )=( 2 1 )

Hence, the value of variable is x=2 and y=1 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
TY D om E h om ng 00 C B A G F Q ו 3 13 Details Find an Euler path for the graph. Enter your response as a sequence of vertices in the order they are visited, for example, ABCDEA. fic ► Question Help: Video Message instructor Submit Question tor arch 園 A Wind advisory
You are provided with three 2D data points, p1, p2 and p3. Solving A C = B for C provides youwith the coefficients of a natural cubic spline curve that interpolates these points.Additionally, you have been given A and B, but some elements are missing. Moreover, the last two rowsof A are entirely absent. Your task is to determine and fill in the missing elements. For the last two rows,enforce a zero tangent at the beginning (in p1) and a not-a-knot boundary condition in p2. The matricesA and B are given as follows:Explain how to find the entries of A and B . How would you adapt these matrices if the data pointswere 3D? What if your spline should go through five data points? How many “extra rows” would there thenbe (with “extra” meaning “in addition to securing C2-continuity”)?
Which graph represents f(x) = √x-2+3?
Knowledge Booster
Background pattern image
Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Intermediate Algebra
Algebra
ISBN:9780998625720
Author:Lynn Marecek
Publisher:OpenStax College
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Text book image
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Inverse Matrices and Their Properties; Author: Professor Dave Explains;https://www.youtube.com/watch?v=kWorj5BBy9k;License: Standard YouTube License, CC-BY