INDUMAT Finals Review

Question 1

In a truth table, what is the mathematical approach in evaluating conjunction (p ʌ q)?

Answer 1

min (p,q)

Question 2

In a truth table, what is the mathematical approach in evaluating disjunction (p v q)?

Answer 2

max (p,q)

Question 3

In a truth table, what is the mathematical approach in evaluating conditional (p → q)?

Answer 3

True if and only if the val (p) is less than or equal to val (q)

Question 4

In a truth table, how do you evaluate a biconditional (p <=> q)?

Answer 4

True if both statements have the same truth value. (Both p and q are true or both q and p are false). Otherwise, it is false.

Question 5

In a truth table, if all the outputs of a column are true, then it is a _________

Answer 5

Tautology

Question 6

In a truth table, if all the outputs of a column are false, then it is a _________

Answer 6

Contradiction

Question 7

In a truth table, if the outputs have at least one true and one false, then it is a _________

Answer 7

Contingent

Question 8

A matrix where elements below the main diagonal are all zeroes

Answer 8

Upper Triangular Matrix (Right Triangular Matrix)

Question 9

A matrix where the elements above the main diagonal are all zeroes

Answer 9

Lower Triangular Matrix (Left Triangular Matrix)

Question 10

Matrix where all elements are zeroes

Answer 10

Null Matrix

Question 11

True or False. A matrix is symmetrical if A = A^T.

Answer 11

True

Question 12

Type of matrix that has a determinant value of zero and does not have an inverse.

Answer 12

Singular Matrix

Question 13

Type of matrix that has a determinant value and has an inverse.

Answer 13

Non-Singular Matrix (Standard Matrix)

Question 14

True or False. Identity matrices are nonsingular.

Answer 14

True

Question 15

If a matrix undergoing an iterative method is not diagonally dominant, then _________.If a matrix undergoing an iterative method is not diagonally dominant, then _________.

Answer 15

You must interchange the rows such that the diagonal consists of the highest coefficients of the matrix.

Question 16

Steps for LU Decomposition

Answer 16

1. Setup matrices as AX=B
2. Get the upper triangular matrix based on A
3. Put the multipliers in the lower triangular matrix (Make sure to negate or make “+” into “-“ and vice versa)
4. Get y values from LY = B
5. Get x values from UX = Y

Question 17

Steps for Inverse Method

Answer 17

1. Setup the matrices as AX = B
2. Find A^-1
3. X = A^-1 B

Question 18

Steps for Gaussian Elimination

Answer 18

1. Setup augmented matrix
2. Use Elementary Row Operations until you create an upper triangular matrix
3. Make sure the main diagonal values are equal to ‘1’.
4. Convert back into equation form
5. Back substitute

Question 19

Steps for Gauss Jordan Method

Answer 19

1. Setup augmented matrix
2. Use Elementary Row Operations until you create an identity matrix
3. Convert back into equation form

Question 20

Steps for Gauss Jacobi

Answer 20

1. Check for diagonal dominance (rearrange rows if found otherwise)
2. Isolate the variables per row based on the diagonal
3. Initialize/ Get k=0 iteration wherein variables are all equal to zero
4. Substitute values into the equations of the variables using values computed from previous iterations
5. Solve for error values (error = absolute value of old-new)
6. Repeat the process until the calculated answer has an error value below the tolerable error.

Question 21

Steps for Gauss Seidel

Answer 21

1. Check for diagonal dominance (rearrange rows if found otherwise)
2. Isolate the variables per row based on the diagonal
3. Initialize/ Get k=0 iteration wherein variables are all equal to zero
4. Substitute values into the equations of the variables using the most recent values
5. Solve for error values (error = absolute value of old-new)
6. Repeat the process until the calculated answer has an error value below the tolerable error.

Question 22

Necessary and Sufficient Conditions for Local Minima (Theorem 1)

Answer 22

1. Equate first derivative to zero
2. Get the extreme points
3. Plug in the extreme points to the second derivative
4. If the value is greater than 0, it is a minima.

Question 23

Necessary and Sufficient Conditions for Local Maxima (Theorem 2)

Answer 23

1. Equate first derivative to zero
2. Get the extreme points
3. Plug in the extreme points to the second derivative
4. If the value is less than 0, it is a maxima.

Question 24

Convex Graph

Answer 24

U

Question 25

Concave Graph

Answer 25

∩

Question 26

Both Concave and Convex

Answer 26

\ or / (Linear Line)

Question 27

Formula and Procedure for Secant Method

Answer 27

1. Assume x0 and x1.
2. If absolute value of f (x0) < f(x1), then swap x0 and x1; otherwise keep it as it is.
3. Solve for x2
4. Set x0 = x1 and x1=x2
   5.Solve for the new x2
5. Continue until less than tolerable error

Formula: x2 = x1-f(x1) [(x1-x0) / f(x1) - f(x0)]

Question 28

Procedure for Bisection Method

Answer 28

1. Make columns (k, a , f(a), b, f(b), m, f(m), and error)
2. Get the value of f(m) wherein m = (a+b) / 2
3. If f(m) is equal to 0, then m is a root.
4. If f(m) is less than 0, set a = m. If f(m) is greater than 0, set b = m.

Question 29

For Secant Method, if the given is a trigonometric function, then calculator must be set to ________ .

Answer 29

Radians