Math 120 Quiz 1 Questions PDF

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Questions for Math 120 quiz that can be used for practice....

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MATH-120

QUIZ 1 F2021

You have 60 minutes to solve and upload (PROPERLY!!!) your SOLUTIONS for Q1 in the window for Q1 and your ANSWERS ONLY for Q2 in the window for Q2 Solve each of the following systems whose augmented matrices are given: 1 −1 0 0 3  1 2 − 1 − 1 0 5 0 1 1 2  0 0 1 1  −7 −1 3    (ii)  0 −1 − 1 − 1 5  0 0 − 1 − 1 2 3      0 0 0 2 −4   0 0 0 0 − 1 2

Q1.

(i)

Q2. For each of the following phrases choose the right continuation out of the options provided. You do not have to explain your choice. UPLOAD the ANSWERS ONLY. 1) then (a) (b) (c) (d)

If for some system in 4 variables the rank of the coefficient matrix is equal to 2, The system has a unique solution The system is inconsistent The system does not have a unique solution The system has exactly 2 solutions

2) A homogeneous system in 5 variables with the rank of the coefficient matrix equal to 5 (a) Will be inconsistent (b) Will have infinitely many solutions (c) Will have only the trivial solution (d) Will have a nontrivial solution.

3)

The following system with parameters a, b

x − 2y + z = 0 − 2x + 3y − z = b y − az = 3 (a) (b) (c) (d)

has infinitely many solutions when a = 1, and b  − 3 if is inconsistent if a = 1, and b = − 3 has infinitely many solutions when a = 1, and b = − 3 has a unique solution if and only a  1, and b  − 3...