Linear Algebra

62 Chapter 1. Linear Systems
(b) This is the Chemistry problem.
7h =7j
8h +1i =5j +2k
1i =3j
3i =6j +1k
2 Use the computer to solve these systems from the first subsection, or conclude
‘many solutions’ or ‘no solutions’.
(a) 2x +2y =5 (b) −x + y =1 (c) x − 3y + z = 1
x − 4y =0 x + y =2 x + y +2z =14
(d) −x − y =1 (e) 4y + z =20 (f) 2x + z + w = 5
−3x − 3y =2 2x − 2y + z = 0
y − w = −1
x + z = 5 3x − z − w = 0
x + y − z =10 4x + y +2z + w = 9
3 Use the computer to solve these systems from the second subsection.
(a) 3x +6y =18 (b) x + y = 1 (c) x1 + x3 = 4
x +2y = 6 x − y = −1 x1 − x2 +2x3 = 5
4x1 − x2 +5x3 =17
(d) 2a + b − c =2 (e) x +2y − z =3 (f) x + z + w =4
2a + c =3 2x + y + w =4 2x + y − w =2
a − b =0 x − y + z + w =1 3x + y + z =7
4 What does the computer give for the solution of the general 2×2 system?
ax + cy = p
bx + dy = q