(a) Show that the nonsingular system ax + by = p, ex -I- dy = q has the solution given by the determinantal ratios

Where

(b) Use Cramer's Rule (1.87) to solve the systems
(i) x + 3y=13.
4x + 2y = 0
(ii) x-2y = 4,
3x + 6y = - 2
(c) Prove that the solution to
ax + by + cz = p.
dx + ey + fz = q,
gx +hy + jz = r.
with

Is

(d) Use Cramer's Rule (1.88) to solve
(i) x + 4y = 3,
4a- + 2y + Z = 2,
- x + y - z = 0,
(ii) 3a + 2y -z - 1,
a -3y + 2z = 2,
2a - y + z = 3.
(e) Can you see the pattern that will generalize to n equations in n unknowns?
Remark: Although elegant, Cramer's rule is not a very practical solution method.

Transcribed Image Text:

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