Definitions Flashcards
What is the definition of a scalar in engineering mathematics?
A scalar is a quantity that is fully described by a magnitude alone.
True or False: A vector has both magnitude and direction.
True
Fill in the blank: The _______ of a vector is a measure of its length.
magnitude
What is the definition of a matrix?
A matrix is a rectangular array of numbers arranged in rows and columns.
What operation combines two matrices of the same dimension by adding their corresponding elements?
Matrix addition
Multiple Choice: Which of the following is a property of a determinant? (A) It can be negative, (B) It is always zero, (C) It is only defined for square matrices.
C
What is the definition of an eigenvalue?
An eigenvalue is a scalar associated with a linear transformation represented by a matrix, indicating how much a corresponding eigenvector is stretched or compressed.
True or False: The dot product of two vectors results in a vector.
False
Fill in the blank: The _______ of a function is the set of all input values for which the function is defined.
domain
What is the definition of a limit in calculus?
A limit is the value that a function approaches as the input approaches a certain point.
Multiple Choice: Which of the following is a method for solving ordinary differential equations? (A) Integration by parts, (B) Separation of variables, (C) Completing the square.
B
What is the definition of a derivative?
A derivative represents the rate of change of a function with respect to a variable.
True or False: The integral of a function gives the area under the curve of that function.
True
Fill in the blank: In numerical analysis, _______ refers to the process of finding approximate solutions to mathematical problems.
approximation
What is the definition of a nonlinear equation?
A nonlinear equation is an equation in which the variable(s) appear with exponents greater than one or are multiplied together.
