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A set of practice questions for college math test 4, including systems of equations, matrix operations, inverses, sequences, binomial theorem, and word problems. It covers various topics that are typically studied in a first-year college math course.
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Math 121, Some Practice Questions for Test 4
0 0 k − 4
(^) represents a system of equations in the vari-
ables x, y, z. (a) For what values of k is there no solution? (b) For what values of k is there exactly one solution? (c) Find the solution to this system of equations if k = −2.
, and C =
. Find the following, if possible, if an operation is not possible, state why it is not possible. (a) BC (b) CB (c) 2A − 2 C
x + y + 2 z = 1 2 x + 3 y + 3 z = − 2 3 x + 3 y + 7 z = 3
Solve this system using the fact that the inverse of
(^) is
(^) and B =
(a) Let C = AB. Determine the dimensions of C, and find c 23 (you don’t need to compute the entire product). (b) Does D = BA exist? If so, determine the dimensions of D and find d 31.
(^) represents a system of equations in the vari-
ables x, y, z. Find the solution to this system of equations.
(^) if it exists.
k=
(−1)k 2 k+^.
2 x − y − z = − 1 −x + 3 y − z = − 3 − 5 x + 5 y + z = − 1
Note. Answers to these questions may be found on your instructor’s website at http://faculty.lasierra.edu/∼jvanderw/classes/m121a06/m121prac4a06ans.pdf Other old tests and review questions are also available at your instructor’s website.