Solving a linear system as a matrix equation Solve the system of equations by converting to a matrix equation and using the inverse of the co-efficient matrix, as in example 6. Use the inverses from Exercises , , , , and .
. Finding the inverse of a matrix Find the inverse of a matrix if it exists.
The system of equations by converting it into a matrix equation and find the values of , , , and .
A system of linear equations can be written in the form of where is called the coefficient matrix, is called the known matrix, and is called the variable matrix.
If a square matrix of dimension has an inverse , and if is a variable matrix and is a known matrix both with rows, then the solution of the matrix equation is given by:
Take a matrix with left half as matrix and right half as and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix .
The system of linear equations can be written as a single matrix equation as follows.
Here , , and .
The solution of this matrix equation is given by .
First find ,
Take a matrix of dimension with left half as matrix and right half as and perform row operations to transform the left half into .
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