Linear Algebra, 2020a

66 Chapter One. Linear Systems
[0,0,2,0,4,0,0],
[0,5,-2,0,0,50,0]] );
> u:=array( [0,0,0,0,10,10,0] );
> linsolve(A,u);
7 2 5 2 5 7
[ -, -, -, -, -, 0, - ]
3 3 3 3 3 3
If a system has infinitely many solutions then the program will return a
parametrization.
Exercises
1 Use the computer to solve the two problems that opened this chapter.
(a) This is the Statics problem.
40h + 15c = 100
25c = 50 + 50h
(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 (d) −x − y = 1
x − 4y = 0 x + y = 2 x + y + 2z = 14 −3x − 3y = 2
(e) 4y + z = 20 (f) 2x + z + w = 5
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
x + 2y = 6
(b) x + y = 1
x − y =−1
(c) x 1 + x 3 = 4
x 1 − x 2 + 2x 3 = 5
4x 1 − x 2 + 5x 3 = 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