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ENGR 391 MIDTERM EXAM ATTEMPT REVIEW CONCORDIA UNIVERSITY
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ENGR 391 MIDTERM EXAM ATTEMPT REVIEW CONCORDIA UNIVERSITY
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ENGR 391 MIDTERM EXAM: ATTEMPT REVIEW CONCORDIA UNIVERSITYQuestion 1
Complete
Not graded
By checking the "yes" answer below I confirm
1. that I have neither given nor received unauthorized aid to answer the questions of this assignment.
2. I agree to follow the rules in regard of online assignments as posted in the course outline
3. I used only octave or Matlab to solve the questions (I am allowed to consult all course material and my
ownnotes)
Select one:
a. Yes I agree
b. No I do not agree
Your answer is correct.
The correct answer is: Yes I agree
,Question 2
Partially correct
Mark 0.50 out of 1.00
Among the following functions, for which of them bracketing methods can not be used?
Select one or more:
3
a. f(x) = x − x+5
2
b. f(x) = (5x − 3)
c. f(x) = 1 − ex
d. f(x) = sin(x2 )
Your answer is partially correct.
You have correctly selected 1.
Reference: first lecture on bracketing methods of lesson 2
3
The correct answers are: f(x) = x − (x) = (5x − 3)2
,f
x+5
, 11/5/21, 4:05 PM Midterm exam: Attempt review
Question 3
Incorrect
Mark 0.00 out of 1.00
b
Consider the linear equation ax = b with solution r = a .
How much is the maximal relative error magnification factor for this equation for the approximation xr of
thesolution r?
Select one:
a. \(|ax_r|\)
b. \(|ax_r-b|\) This is the absolute
backward error
c. 1
d. \(|a|\)
Your answer is incorrect.
Written in matrix form the system writes: \([a]x=[b]\). Here the coefficient matrix \(A\) is a 1x1 matrix.
The maximal error magnification factor is given by the conditioning number of the coefficient matrix
\(A\).In our case the coefficient matrix \(A\) is \([a]\).
So \( cond(A)=\Vert A \Vert \cdot \Vert A^{-1} \Vert = \Vert [a] \Vert \cdot \Vert [a^{-1}] \Vert = |a| \cdot \frac{1}
{|a|} = 1 \)
The correct answer is: 1
Question 4
Incorrect
Mark 0.00 out of 1.00
\( \Vert Ax \Vert_\infty = \Vert A \Vert_\infty \cdot \Vert x
\Vert_\infty \)Select one:
True
False
This is false. In fact we have \( \Vert Ax \Vert_\infty \leq \Vert A \Vert_\infty \cdot \Vert x
\Vert_\infty \)The correct answer is 'False'.
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