College Algebra, 2013a

590 Systems of Equations and Matrices
Recall that the entries to the left of the vertical line come from the coefficients of the variables in
the system, while those on the right comprise the associated constants. For that reason, we may
form the coefficient matrix A, theunknowns matrix X and the constant matrix B as below
⎡
A = ⎣
3 −1 1
1 2 −1
2 3 −4
We now consider the matrix equation AX = B.
⎡
⎣
⎤
3 −1 1
1 2 −1
2 3 −4
⎡
⎣
⎡
⎦ X = ⎣
⎤ ⎡
⎦ ⎣
x
y
z
⎤
AX = B
x
y
z
3x − y + z
x +2y − z
2x +3y − 4z
⎤
⎦ =
⎤
⎦ =
⎡
⎦ B = ⎣
We see that finding a solution (x, y, z) to the original system corresponds to finding a solution X
for the matrix equation AX = B. If we think about solving the real number equation ax = b, we
would simply ‘divide’ both sides by a. Is it possible to ‘divide’ both sides of the matrix equation
AX = B by the matrix A? This is the central topic of Section 8.4.
⎡
⎣
⎡
⎣
8
4
10
8
4
10
⎤
⎦
⎤
⎦
8
4
10
⎤
⎦