To solve: The system of equations algebraically by any method.
Answer to Problem 82AYU
Solution:
The system of equations has infinite solutions.
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 system of equations has infinite solutions.
Chapter 11 Solutions
Precalculus
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