Solutions to various problems can be obtained easily by representing the problem in the form of matrix equations and then solving it.
What are Matrix Equations?
If a variable is used to represent a matrix in an equation, then it is called as a matrix equation.
Solving Matrix Equations
How to solve matrix equations? If the matrix equations are simple, then they can be solved using Matrix Addition or Scalar Multiplication.
Matrix addition or elimination method is a method of eliminating the matrix on the left side so that only “X” is in the left side and the corresponding answer in the right side. To achieve this, a matrix identical to the one present on the left side is subtracted on both left and right sides.
Scalar multiplication refers to the method of multiplying every entry or element in the given matrix with a scalar i.e. a constant.
Solving Systems of Equations with Matrices
To solve systems of equations with matrices, the equations are first written in the form of matrices and then they are solved. Listed below is the step by step procedure for solving systems of complex matrix equations:
1. Left side of the matrix is considered first. The variables and the coefficient of the variables are taken separately and the matrix is formed on the left side. It is written as a product of two matrices, one is a coefficient matrix and the other one is a variable matrix.
2. The constant of the equations forms a matrix and it is written on the right side of the equation.
Therefore, the equation will be in the form of:
COEFFICIENT MATRIX x VARIABLE MATRIX = CONSTANT MATRIX
3. Now to solve the equation, the inverse of the coefficient matrix is derived.
4. Either side of the equation is multiplied with the inverse matrix. The inverse matrix must be placed in front of the already available matrix as matrix multiplication does not satisfy commutative property.
5. The result will be the product of an identity matrix, the variable matrix on the left side and the resultant constant matrix on the right side. The identity matrix shows that the inverse matrix is correct. The values in the constant matrix are then assigned to the corresponding variables in the variable matrix.
The Gauss Jordan Method helps to solve systems of equations with matrices. In the Gauss Jordan Method, the initial expanded matrix on the left side is finally converted into an identity matrix. The right side matrix containing the values for the variables is assigned to the corresponding variables.
What are Matrix Equations?
If a variable is used to represent a matrix in an equation, then it is called as a matrix equation.
How to solve matrix equations? If the matrix equations are simple, then they can be solved using Matrix Addition or Scalar Multiplication.
Matrix addition or elimination method is a method of eliminating the matrix on the left side so that only “X” is in the left side and the corresponding answer in the right side. To achieve this, a matrix identical to the one present on the left side is subtracted on both left and right sides.
Scalar multiplication refers to the method of multiplying every entry or element in the given matrix with a scalar i.e. a constant.
Solving Systems of Equations with Matrices
To solve systems of equations with matrices, the equations are first written in the form of matrices and then they are solved. Listed below is the step by step procedure for solving systems of complex matrix equations:
1. Left side of the matrix is considered first. The variables and the coefficient of the variables are taken separately and the matrix is formed on the left side. It is written as a product of two matrices, one is a coefficient matrix and the other one is a variable matrix.
2. The constant of the equations forms a matrix and it is written on the right side of the equation.
Therefore, the equation will be in the form of:
COEFFICIENT MATRIX x VARIABLE MATRIX = CONSTANT MATRIX
3. Now to solve the equation, the inverse of the coefficient matrix is derived.
4. Either side of the equation is multiplied with the inverse matrix. The inverse matrix must be placed in front of the already available matrix as matrix multiplication does not satisfy commutative property.
5. The result will be the product of an identity matrix, the variable matrix on the left side and the resultant constant matrix on the right side. The identity matrix shows that the inverse matrix is correct. The values in the constant matrix are then assigned to the corresponding variables in the variable matrix.
The Gauss Jordan Method helps to solve systems of equations with matrices. In the Gauss Jordan Method, the initial expanded matrix on the left side is finally converted into an identity matrix. The right side matrix containing the values for the variables is assigned to the corresponding variables.
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