Matrix Algebra Review
Math
DANIEL A. FLEISCH, "Matrix Algebra Review"
Sample Data
| Front | Solve simultaneous linear equations using the Cramer’s Rule
 |
| Back | In general, three linear equations in three unknowns (x1 , x2 , x3) can be written as
 or
 If you define the matrices
 and
 and
 then the system of equations can be written as a single matrix equation:
 The first unknown (x1 in this case) is found by replacing the values in the first column of the coefficient matrix (A) with the elements of matrix b and dividing the determinant of that matrix by the determinant of A. Here’s how that looks:
 Likewise, to find the second unknown (x2 in this case), replace the values in the second column of A with the elements of b:
 and to find x3 use
 Thus for the equations given,
 and
 Hence
 so
 Proceeding in the same way for y and z gives
 so
 and
 so
 |
| Front | “null” or “zero” matrix |
| Back | a matrix with all elements equal to zero
 |
| Front | multiplying a row vector A by a column vector B |
| Back |
 |