=E2=88=8F is a symbol used in Lagrange Interpolating polynomial which designates

- pi
- =E2=80=9Cthe inverse of=E2=80=9D
**=E2=80=9Ca product of=E2=80=9D**Correct- =E2=80=9Cthe sum of=E2=80=9D

A column vector is denoted by a boldface lowercase letter and expressed as

- 1 x n matrix
**n x 1 matrix**Correct- no correct answer
- m x n matrix

A continuous function's integral is approximated using either the trapezoidal or Simpson's rule by translating the function into discrete form

**True**Correct- False

A cubic polynomial can interpolate three points

- True
**False**Correct

A diagonal matrix could be an identity matrix if the diagonals have a value of

- any non-zero
**1**Correct- no correct answer
- 0

A Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose and can be decomposed using Cholesky’s method.

**True**Correct- False

A mathematical model that will compute the following limit as will readily give _____________ answer.

- 0
- infinite
**indeterminate**Correct- finite

A matrix decomposition method that has an upper triangular matrix and an orthogonal matrix is referred to as the QR

**True**Correct- False

A matrix is symmetric/ Hermitian positive definite matrix if

- No correct answer
- the resulting triangular factors are equal to each other
- the resulting triangular factors are the negative value of each other
**the resulting triangular factors are the transpose of each other**Correct

A matrix which is denoted by a boldface lowercase letter and expressed as 1 x n matrix is

- no correct answer
**column vector**Correct- row vector
- not a matrix

A root finding method also known as the Tangent method is

**Newton's method**Correct- Open method
- Secant Method
- Bisection method

A root finding method which requires the function to be differentiable

**Newton-Raphson iteration**Correct- Bisection
- False position
- Secant Method

A row vector is denoted by a boldface lowercase letter and expressed as a

**1 x n matrix**Correct- m x n matrix
- n x 1 matrix
- no correct answer

A square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is less than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row.

**True**Correct- False

Algorithms should have explicitly defined set of inputs and outputs

**True**Correct- False

Also called trapezoidal rule It approximates the area under a curve by atrapezoidwith horizontal base and sloped top (connecting the endpointsx1andx2)

**2-point closed Newton-Cotes formula**Correct- Newton-Raphson
- Gauss-Seidel
- Gauss-Jordan

Among the many applications of matrices are used in statistics, economics, physics, and engineering.

**True**Correct- False

An additional benefit of the power method is that the corresponding eigenvector is obtained as a by-product of the method.

**True**Correct- False

An algorithm design technique is a general approach to solving problems algorithmically that is applicable to a variety of problems from different areas of computing

**True**Correct- False

An integral expressed as the difference between the values of the integral at specified upper and lower limits of the independent variable

- indefinite integral
- improper integral
- proper integral
**definite integral**Correct

Another condition that must be satisfied is that the diagonal elements are all nonzero for the Gauss-Seidel method to be used:

**True**Correct- False

Another method called midpoint rule is an open type method numerical integration

**True**Correct- False

Approximating calculations which involve infinite value, most often used in series notations and in calculus doesn't introduce errors.

- True
**False**Correct

Best-case is the maximum number of steps taken on any instance of size of a variable

- True
**False**Correct

By applying the power method to the matrix inverse of [A], the power method will ________on the largest value of 1/λ in other words, the smallest value of λ

- no correct answer
- diverge
**converge**Correct- fail

Cholesky’s Method is based on the fact that a symmetric matrix can be decomposed into triangular factors are the transpose of each other.

**True**Correct- False

Choosing an initial guess which gives near f(x) = 0 is considered a good guess

**True**Correct- False

Compute for the determinant of the 2 x 2 matrix defined as

- D = 125
**D = 0875**Correct- No correct answer
- D = - 0675

Creating a mathematical model that will compute the following limit as will produce a result of

- 0
**1**Correct- indeterminate
- infinite

Direct method for finding the eigenvalues is recommended since the calculation of zeros of a polynomial is numerically challenging if not unstable.

**True**Correct- False

Each component of the new iterates in Gauss-Seidel method depends upon all previously computed components, the updates cannot be done simultaneously.

**True**Correct- False

Eigenvalues are used in the analysis of linear transformation such as scaling.

**True**Correct- False

Find the missing value to satisfy that y = 1/24x +2y +2z = 8x + 4y - 2z = ?3x +y - z = 4

- 4
- 05
- 3
**2**Correct

First order differences is equivalent f[x0,x1] when i = 0

**True**Correct- False

For is the iteration may terminate if the difference between f (x) is already zero.

**True**Correct- False

For a two segment trapezoidal rule, it will use the points similar to the ones used by Simpson's 1/3 rule

**True**Correct- False

For an interval of 0 to 1, a subinterval with a size of 02 will give n = 5 described as 5 segment Trapezoidal rule

**True**Correct- False

For both the Trapezoidal and Simpson's 1/3 rule , using more strips will give better approximation of the curve

**True**Correct- False

For practical reasons, the absolute error is usually more meaningful than the relative error.

- True
**False**Correct

For the function , its first derivative is f’(x) is

**True**Correct- False

For the function f(x) =its first derivative is f’(x) is The first derivative of the function is f’(x) =

**True**Correct- False

For the function f(x) = ex-2 the next approximated value of the root when x0 = -1 and x1 = 1 is x2 = 0.98626.

**True**Correct- False

For the function f(x) = ex-2 the value of f(x2) when x0 = -1 and x1 = 1 is f(x) = -0.5248

**True**Correct- False

For the given systems of linear equations, with initial values x1 =0; x2 =0; x3 = 0. The next iterative value of x1 using Gauss-Seidel Method is 1.3333.

**True**Correct- False

For the given systems of linear equations, with initial values x1 =0; x2 =0; x3 = 0. The next iterative value of x2 using Gauss-Seidel Method is 1.5.

**True**Correct- False

For the given systems of linear equations, with initial values x1 =0; x2 =0; x3 = 0. The next iterative value of x3 using Gauss-Seidel Method is 0.5278.

**True**Correct- False

From the two data points (1,4) and (3, 7), and (4,10) using Lagrange polynomial method, the polynomial is Li(x) = 05x2-05x +2

- True
**False**Correct

From the two data points(2,5) and (6, 11), using Lagrange polynomial method, the polynomial is Li(x) = 15x +2

**True**Correct- False

Gauss-Jordan method consists of guessing a value and then using a systematic method to obtain a refined estimate of the root.

**True**Correct- False

Gaussian elimination has no specific row operations Various ways can be employed but may come up with the same answer

**True**Correct- False

Given a matrix A , its QR -decomposition is an upper triangular matrix and an orthogonal matrix. An orthogonal matrix is a matrix whose transpose is equivalent to its inverse.

**True**Correct- False

Given the function f(x) = 075 + 11x, an exact value can be given instantly by Trapezoidal rule

**True**Correct- False

Horner’s method which is a method for finding roots of a polynomial equation f(x) =0 is almost similar to Newton’s method.

**True**Correct- False

How much error would be observed for the integral of f(x) = sin2x + 5 for an interval of [0,1] if n = 1 or if n = 2?

- approximately 05
- approximately 1
- greater than 1
**almost negligible**Correct

If A is a 3 x 3 matrix and B is a 3x2 matrix , the statement “ A – B is not possible” is

**True**Correct- False

If a matrix has its entire diagonal elements are positive, then the real parts of its eigenvalues are negative.

**True**Correct- False

If A−1 (if it exists) the eigenvalues of A−1 is 1/5, 1/4 and 1/2 if matrix A has eigenvalues 5, 4 and 2

**True**Correct- False

If A−1 (if it exists) the eigenvalues of A−1 is 1/5, ¼ and ½ if matrix A has eigenvalues 5, 4 and 2.

**True**Correct- False

If matrix A gives the largest eigenvalue, it suggests that if A -1 exists, the smallest eigenvalue can be obtained through inverse power method.

**True**Correct- False

If matrix A is invertible such that A−1 = L−TL−1 then matrix A can be decomposed using Cholesky’s method.

**True**Correct- False

If matrix is A is positive definite then a11 > 0.

**True**Correct- False

If QT is the transpose of Q then QT Q = I or the identity matrix.

**True**Correct- False

If the determinant of the matrix is zero, it is impossible to check the solutions of the variables using

- Gaussian Elimination method
- Neither "Cramer's Rule" nor "Gaussian Elimination method" is correct
**Cramer's Rule**Correct- Both "Cramer's Rule" and "Gaussian Elimination method" are correct

If the eigenvalues are repeated roots λ1 = λ2 = λ3, then the characteristic polynomial is of

- 2nd degree polynomial
**3rd degree polynomial**Correct- is an n-1 polynomial
- no correct answer

If the function, f(x) = cos3x was approximated by the polynomial, P(15) = -02, the amount of error approximately 005

**True**Correct- False

If the interval of the function is given as 0 to pi, for n = 6 segments, each node or segments will be

**True**Correct- False

If the magnitude of the diagonals is greater than the sum of the non-diagonals in the same row, then the matrix is not diagonally dominant.

**True**Correct- False

If the main determinant is zero the system of linear equations is

**Both "inconsistent" and "has infinite many solutions" are correct**Correct- Has infinite many solutions
- Inconsistent
- Neither "inconsistent" nor "has infinite many solutions" is correct

If the number of segments, n= 20 Compute for the stepsize, h if the interval is from 0 to 1

- h = 05
**h = 005**Correct- h = 020
- h = 002

If the tridiagonal coefficient matrix is diagonally dominant, then procedure Tri

- no correct answer
- will diverge
**will encounter zero divisors**Correct- will not encounter zero divisors

If there is a randomized algorithm that solves a decision problem in time t and outputs the correct answer with probability 05, then there is a randomized algorithm for the problem that runs in time =CE=98(t) and outputs the correct answer with probability at least 099

- True
**False**Correct

If x2 is the approximated root in Secant method, it follows that; the value of f(x2) must be equal to 0.

**True**Correct- False

If you need to evaluate a definite integral involving a function whose anti derivative cannot be found, it is easier to resort to this approximation technique

- Direct Method
- Cholesky's Method
- Power Method
**Trapezoidal method**Correct

In creating a computer algorithm one important factor that should be considered is that the user would be prompted the values that are needed in solving.

**True**Correct- False

In differentiation using numerical methods, one of the steps is interpolating the function by a polynomial p at suitable points

**True**Correct- False

This course is taught by the mentor:

Master of Arts in Mathematics Education specialization in College Teaching.

All courses