D420 Discrete Math: Functions and Relations - Set 2 - Part 2

Correct Answer: A tree that explores the graph by distance from the start vertex

Breadth-first search explores the graph by expanding the tree to include vertices that are closest to the start vertex.

Correct Answer: It finds the minimum spanning tree by starting at a vertex and growing the tree by adding the smallest edge

Prim's algorithm is a greedy algorithm that finds the minimum spanning tree by starting at a vertex and adding the smallest possible edge to grow the tree.

Correct Answer: It is a nonsingular matrix

A nonsingular matrix is a square matrix that has an inverse, meaning it can be multiplied by another matrix to yield the identity matrix.

Correct Answer: A square matrix where all non-diagonal entries are zero

A diagonal matrix is a square matrix where the only nonzero entries are along the main diagonal.

Correct Answer: The number of columns in the first matrix must equal the number of rows in the second matrix

For matrix multiplication to be defined, the number of columns in the first matrix must match the number of rows in the second matrix.

Correct Answer: A diagonal matrix where all diagonal elements are 1

The identity matrix is a diagonal matrix with 1s on the diagonal and 0s elsewhere. It acts as the multiplicative identity in matrix multiplication.

Correct Answer: To reduce a matrix to row echelon form

Gaussian elimination is a method used to reduce a matrix to row echelon form by applying a series of row operations.

Correct Answer: The number of non-zero rows in its row echelon form

The rank of a matrix is the number of non-zero rows in its row echelon form, which represents the dimension of the row space.

Correct Answer: A matrix that includes an extra column representing the constants from a system of equations

An augmented matrix is formed by appending the constant terms from a system of linear equations to the coefficient matrix.

Correct Answer: It converges if the common ratio is less than 1

The sum of a finite geometric series converges if the common ratio is less than 1.

Correct Answer: A series that diverges to infinity

A harmonic series grows very slowly but diverges to infinity.

Correct Answer: 1, 3, 5, 7,

An arithmetic sequence is one where each term is obtained by adding a constant value to the previous term, as in 1, 3, 5, 7,

Correct Answer: 3

The common difference in this arithmetic sequence is 3, as each term is obtained by adding 3 to the previous term.

Correct Answer: A sequence in which each term is multiplied by a constant to obtain the next term

A geometric sequence is one in which each term is obtained by multiplying the previous term by a constant factor.

Correct Answer: an=3.2n1

The explicit formula for a geometric sequence is an=a1.rn1, where a1 is the first term and r is the common ratio.

Correct Answer: A series with a limited number of terms

A finite series is a series that has a specific number of terms.

Correct Answer: It converges if the common ratio is less than 1

An infinite geometric series converges if the absolute value of the common ratio is less than 1.

Correct Answer: A function that is injective and surjective

A bijection is a function that is both injective and surjective (onto).

Correct Answer: It exists if the function is bijective

A function has an inverse if it is bijective, meaning it is both injective and surjective.

Correct Answer: A function where each element in the domain maps to a unique element in the codomain

An injective function is one where no two distinct elements in the domain map to the same element in the codomain.