W2 Assignment: True or False Submissions accepted: 2/27/ XXXXXXXXXX:00 AM Review: Full, Anonymous: No Finite Mathematics True or False If you think the statement is true, then show that it is true. On...

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W2 Assignment: True or False
Submissions accepted: 2/27/2013 1 12:00 AM Review: Full, Anonymous: No
Finite Mathematics
True or False
If you think the statement is true, then show that it is true. On the other hand, if you think the statement is false, then give an example that disproves the statement. For example, the statement "If A and B are matrices of the
same order, then A - B = B - A" is false and an example that disproves it is A 1 3 4., 4 an.:1 U 1 2 2 1
For
[1 2] A — B 3 4
while
2] 01 [1 2 1 [0 1 3
1 B — A = 12 [ 2] 11 [3 2] 4 [ 0 — 1 0- —3_ A — B
Such an example is called a counterexample.
1 True or false: A system comprising two linear equations in two variables has a unique solution if and only if the straight lines represented by the equations are nonparallel. 2. True or false: Suppose the straight lines represented by a system of two linear equations in two variables are parallel to each other. Then the system has infinitely many solutions. 3. True or false: If A and B are matrices of the same order, then (A +B) r = Ar + r 4. True or false: If A and B are matrices such that AB and BA are both defined, then A and B must be square matrices.
S. True or false: If A is a square matrix with inverse -A-1 and r, is a nonzero real number, then 1 I -1 (cil)
6. True or false: If AX = B is a system of n linear equations in n unknowns and --=-1 does not exist, then AX B does not have a unique solution.
Criteria Grade 0 e 0 Answers are correct. Questions are answered completely. Strategies used to answer questions are appropriate. 80%-100% 0 e 0 Answers are mostly correct. Most questions are answered completely. Most strategies used to answer questions are appropriate. 6O%-79°!o 0 o Some answers are correct. Some Questions are answered completely and work is partially shown. 10%-59%
https://angel.grantham.edu/Seetion/Content/Dropbox.aspx?Entrykl=6071.6A8415F74DC... 2013/03/04
Answered Same DayDec 22, 2021

Answer To: W2 Assignment: True or False Submissions accepted: 2/27/ XXXXXXXXXX:00 AM Review: Full, Anonymous:...

David answered on Dec 22 2021
140 Votes
1.
    
The statement is true
The proof of above can be given in two cases
Case 1: Let the system of linear equations in two variables has
a unique solution then it is required to prove that the straight lines represented by the equations are non-parallel.
Proof: As it is given that
the system of linear equations in two variables has a unique solution
Þ
there is only one common point between two lines
Þ
the lines are intersecting at a point
Þ
if two lines have one common point(or intersecting) then they can’t be parallel, because parallel lines can’t have any common point
Therefore the lines are non-parallel.
Conversely let the straight lines represented by the equations are non-parallel it is required to prove that the system of linear equations in two variables has a unique solution
Proof: As it is given that
the straight lines represented by the equations are non-parallel
Þ
the lines are intersecting
Þ
two lines can intersect atmost at one point only
Þ
these two lines has exactly one common point
Therefore the system of linear equations in two variables has a unique solution
Hence proved
    2.
    
    
    The statement is False
Example: let the system of two linear equations in two variables which are parallel are
3x +2y + 6 =0 and
6x + 4y - 6 = 0
The above two lines are parallel but they are not having infinite many solutions.
It is clear from the graph...
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