13.6 MATRIX SOLUTION OF A LINEAR SYSTEM.  Examine the matrix equation below.  How would you solve for X?  In order to solve this type of equation,

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Presentation transcript:

13.6 MATRIX SOLUTION OF A LINEAR SYSTEM

 Examine the matrix equation below.  How would you solve for X?  In order to solve this type of equation, we need the of the matrix that is multiplied by X.  A matrix times it’s inverse is the matrix: inverse identity

Inverse Matrix  The inverse of 2X2 matrix is found by the following:  If the determinant of A is, then there is no inverse and we call this a singular matrix. zero

Find the inverse of the matrix. If the matrix is singular, state so. 1.2.

Solving Matrix Equations  We use inverses when solving matrix equations like the opening example.  For matrix equation, in order to get X by itself we need to LEFT multiply both sides of the equation by the inverse of A ( ).  This would look like.

3. Solve the opening example

Solve for matrix X. 4.

Solving a System  We can also use this method for solving a system of equations.  For the following system,  The system in matrix form would look like:

 In order to solve the system we need to multiply both sides by the of the coefficient matrix. Solve the system! inverse

5. Solve the system using a matrix equation.