To slove: System of equation using matrix inverse.
Answer to Problem 59AYU
and .
Explanation of Solution
Given:
Calculation:
The original system of equations can be written compactly as a matrix equation.
Where,
and .
To solve the for , and , 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: Sequentially transforming the matrix into reduced row echelon form.
Step 3: Separate the matrix on the right of the vertical bar which is the inverse of .
Hence, the inverse of is
Solving , and .
The solution for the given system of equations is and .
Chapter 11 Solutions
Precalculus
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