MAE 284 Exam Questions AND Correct Answers
A bracket with opposite-signed function values always contains exactly one root(T/F) - ✔✔False
A false position method is based on the false assumption that the function can be approximated by a(n)
- ✔✔straight line
A system of equations can be written in the form: Ax=b, where A is a square matrix, x is a vector of
unknowns, and b is a vector of constants (T/F) - ✔✔True
adaptive Quadrature adjusts to use a smaller step size in areas where the function changes rapidly, and
a larger step size where the function changes slowly.(T/F) - ✔✔True
Adaptive Qudrature uses more segments in regions where the function changes slowly(T/F) - ✔✔False
All mathematical problems have closed-form solution(i.e. they can be solved for a variable having to
make guesses) (T/F) - ✔✔False
All variables that have been defined are found in the command window, even empty ones(T/F) -
✔✔False
Anonymous functions need to be defined before being used(T/F) - ✔✔True
At the start of Guass elimination, the first equation is known as the pivot equation and the a11 element
is known as the pivot element(T/F) - ✔✔True
Bracketing methods always converge, but usually do so more slowly than open methods(T/F) - ✔✔True
Eigenvalues indicate how fast a stable mode decays since the response can be written as x(t)=Ce^ht
(T/F) - ✔✔True
, For the fourth iteration in the Newton-Raphson method, you will use the estimated root location from
the third iteration as the new initial point(T/F) - ✔✔True
Given two vectors a and b, which command would you use to calculate the cross product of a and b? -
✔✔cross(a,b)
How many inputs are in the following function? [a,b] = quiz1(c,d,e,f,g) - ✔✔5
If one row of a matrix consists entirely of zeros, then the determinant is zero(T/F) - ✔✔True
If the determinant of a matrix is zero, the inverse of the matric is a scalar.(T/F) - ✔✔False
If the determinant of a matrix is zero, the matrix is NOT singular.(T/F) - ✔✔False
If the error of an integration technique is proportional to h^2, we say the error of order h^2, which we
write as O(h^2)(T/F) - ✔✔True
If two rows of a matrix are identical, the determinant is zero.(T/F) - ✔✔True
In general, ____________ the step size, h, will decrease the error in a numerical approximation of a
derivative. - ✔✔Decreasing
In general, which of the following will take more time to calculate the solution for a stiff system? -
✔✔An explicit adaptive algorithm(ode45)
Initial value problems have all necessary conditions given at a single value of the independent variable.
(T/F) - ✔✔True
MATLAB's built in fzero function can be used to find the roots, if any, of an equation of the form f(x)=c
(T/F) - ✔✔True
A bracket with opposite-signed function values always contains exactly one root(T/F) - ✔✔False
A false position method is based on the false assumption that the function can be approximated by a(n)
- ✔✔straight line
A system of equations can be written in the form: Ax=b, where A is a square matrix, x is a vector of
unknowns, and b is a vector of constants (T/F) - ✔✔True
adaptive Quadrature adjusts to use a smaller step size in areas where the function changes rapidly, and
a larger step size where the function changes slowly.(T/F) - ✔✔True
Adaptive Qudrature uses more segments in regions where the function changes slowly(T/F) - ✔✔False
All mathematical problems have closed-form solution(i.e. they can be solved for a variable having to
make guesses) (T/F) - ✔✔False
All variables that have been defined are found in the command window, even empty ones(T/F) -
✔✔False
Anonymous functions need to be defined before being used(T/F) - ✔✔True
At the start of Guass elimination, the first equation is known as the pivot equation and the a11 element
is known as the pivot element(T/F) - ✔✔True
Bracketing methods always converge, but usually do so more slowly than open methods(T/F) - ✔✔True
Eigenvalues indicate how fast a stable mode decays since the response can be written as x(t)=Ce^ht
(T/F) - ✔✔True
, For the fourth iteration in the Newton-Raphson method, you will use the estimated root location from
the third iteration as the new initial point(T/F) - ✔✔True
Given two vectors a and b, which command would you use to calculate the cross product of a and b? -
✔✔cross(a,b)
How many inputs are in the following function? [a,b] = quiz1(c,d,e,f,g) - ✔✔5
If one row of a matrix consists entirely of zeros, then the determinant is zero(T/F) - ✔✔True
If the determinant of a matrix is zero, the inverse of the matric is a scalar.(T/F) - ✔✔False
If the determinant of a matrix is zero, the matrix is NOT singular.(T/F) - ✔✔False
If the error of an integration technique is proportional to h^2, we say the error of order h^2, which we
write as O(h^2)(T/F) - ✔✔True
If two rows of a matrix are identical, the determinant is zero.(T/F) - ✔✔True
In general, ____________ the step size, h, will decrease the error in a numerical approximation of a
derivative. - ✔✔Decreasing
In general, which of the following will take more time to calculate the solution for a stiff system? -
✔✔An explicit adaptive algorithm(ode45)
Initial value problems have all necessary conditions given at a single value of the independent variable.
(T/F) - ✔✔True
MATLAB's built in fzero function can be used to find the roots, if any, of an equation of the form f(x)=c
(T/F) - ✔✔True
