3 by 3 matrix system of equations solver

However in the case of just 2 equations, it cannot be dependent. If you have fewer variables than equations, you would have an overdetermined system and will be classified as independent, dependent, or inconsistent. If you have more variables than equations, you would have an underdetermined system and will be classified as dependent or inconsistent. A square system can be classified as independent, dependent, or inconsistent. You can solve a square system of 2 linear equations using Cramer's Rule or Reduced Row Echelon Form.Ī square system has the same number of equations as variables. (Remembering that #I# is the identity matrix.

Now, to solve your matrix equation #A*U=B# you can multiply both sides by the inverse of #A#, i.e. You can check that this representation with matrices represents the system by doing the multiplication #A*U# and setting it equal to #B# you'll get back your original system!!! Where #A# is the matrix of the coefficients of the unknowns, #U# is the column of the unknown and #B# is the column of the pure coefficients (without unknowns). You can use matrices and change your system in a matrix equation : With a system of #n# equations in #n# unknowns you do basically the same, the only difference is that you have more than 1 unknown (and equation) that can now be represented by matrices and by the inverse matrix in place of the coefficient to the -1 (in our example is #3^-1#). To solve this equation you simply take the #3# in front of #x# and put it, dividing, below the #6# on the right side of the equal sign.Īt this point you can 'read' the solution as: #x=2#. Consider a normal equation in #x# such as:

3 by 3 matrix system of equations solver