To solve: The system of equations algebraically by any method.
Answer to Problem 81AYU
Solution:
Unique solution of the given system of equation does not exist.
But, can be written as and where is any real number.
Explanation of Solution
Given:
Calculation:
The original system of equations can be written compactly as a matrix equation.
Where,
To solve the for the solution of has to be found as given below:
Multiply both sides by .
By association property of matrix multiplication, the above equation can be rewritten as:
By the definition of inverse matrix .
By the property of Identity matrix, .
Hence,
i.e. .
Determining .
Step 1: Construction of .
Step 2: Transform the matrix into reduced row echelon form.
The matrix is sufficiently reduced for it to be clear that the identity matrix cannot appear to the left of the vertical bar. So is singular and has no inverse.
The given system of equation has no unique solution. Further, implies where is any real number.
Chapter 11 Solutions
Precalculus
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Calculus & Its Applications (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus
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