Matrix%20Equations

1
Matrix Equations

• Step 1 Write the system as a matrix equation.
  A three-equation system is shown below.

2
Matrix Equations

• Step 2 Find the inverse of the coefficient
  matrix.Note This can be done easily for a 2 x
  2 matrix. For larger matrices, use a calculator
  to find the inverse.

3
Matrix Equations

• Step 3 Multiply both sides of the matrix
  equation by the inverse.The inverse of the
  coefficient matrix times the coefficient matrix
  equals the identity matrix.

Note The multiplication order on the right side
is very important. We cannot multiply a 3 x 1
times a 3 x 3 matrix!
4
Matrix Equations

• Example Solve the system 3x - 2y 9 x
  2y -5

5
Matrix Equations

• Example, continued

Multiply the matrices (a 2 x 2 times a 2 x
1) first, then distribute the scalar.
6
Matrix Equations

• Example 2 Solve the 3 x 3 system 3x - 2y z
  9 x 2y - 2z -5 x y - 4z -2

Using a graphing calculator,
7
Matrix Equations

• Example 2, continued