A/ 1) For what value of "k" will this system have nontrivial solutions?

2) If k = 5 how many solutions are there for # 1 ?

3) Solve the systems:

B/

1) Write this system in the form AX = B.
2) Find det (A)
3) Does A^–1 exist? Why or why not?
4) If A^–1 exists, find it using row reduction.
5) Find solutions for AX = B using your answer from part 4.

C/

1) Can you use Cramer's rule to solve this system? Why or why not?

2) If you can, solve using Cramer's rule.

Solutions

A/

1) solution steps:

a) R₃ – 2R₁; b) switch (– R₁) and R₂; c) R₂ – 2 R₁; d) R₂/11; e) R₃ + 5R₂;

row 3 ends up as 0 0 k – (95/11) and must = 0 so k = 95/11 will give non-trivial solutions.

2) if k = 5 there is a unique solution.

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3) a) b)

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B/

1) ,

2) det A = 3,

3) A^–1 exists because det A is not = 0.

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C/

1) We can use Cramer's Rule since det A = 6.

2) x = 4, y = –2, z = 3

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(Linear Algebra MathRoom Index)

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