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Published byDeirdre Jennings Modified over 9 years ago

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13.6 MATRIX SOLUTION OF A LINEAR SYSTEM

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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

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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

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

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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.

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3. Solve the opening example

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Solve for matrix X. 4.

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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:

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

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5. Solve the system using a matrix equation.

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