Answer:
The statement is true that any linear combination of vectors can always be written in the form Ax for suitable matrix A and vector x.
Step-by-step explanation:
Let
a1x1 + a2x2 + a3x3 + ... + anxn = d1
b1x1 + b2x2 + b3x3 + ... + bnxn = d2
.
.
.
c1x1 + c2x2 + c3x3 + ... + cnxn = dn
be a linear system, and let
[a1 a2 a3 ... an][x1] = [d1]
[b1 b2 b3 ... bn][x2] [d2]
[. . . .
[. . . .
[. . . .
[c1 c2 c3 ... cn][xn] [dn]
be the augmented matrix of the linear system. The augmented matrix can be represented as Ax = d
Where A is the matrix of (a1, a2,...., an), x is (x1, x2, x3, ..., xn), and d = (d1, d2, d3,..., dn) .
The solution set to the linear system is the same as the solution set of Ax = d.
