Matrix Algebra Flashcards
(25 cards)
What is a matrix?
A matrix is a rectangular array of numbers or symbols arranged in rows and columns.
True or False: A matrix can only contain numbers.
False
What is the order of a matrix?
The order of a matrix is defined by the number of rows and columns it contains, expressed as ām x nā.
Fill in the blank: The determinant of a 2x2 matrix [[a, b], [c, d]] is ____.
ad - bc
What operation is performed to find the inverse of a matrix?
The matrix must be multiplied by its adjugate and divided by its determinant.
True or False: The inverse of a matrix A is denoted as A^-1.
True
What is matrix multiplication?
Matrix multiplication is an operation where two matrices are multiplied to produce a third matrix by taking the dot product of the rows and columns.
What is a square matrix?
A square matrix is a matrix with the same number of rows and columns.
Multiple Choice: Which of the following is a property of matrix addition? A) Commutative B) Associative C) Both A and B
C) Both A and B
What is the identity matrix?
The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.
Fill in the blank: The rank of a matrix is the dimension of its ____.
row space or column space
True or False: A singular matrix has an inverse.
False
What does it mean for two matrices to be compatible for multiplication?
The number of columns in the first matrix must equal the number of rows in the second matrix.
What is a transpose of a matrix?
The transpose of a matrix is obtained by swapping its rows and columns.
Multiple Choice: Which of the following is used to solve systems of linear equations? A) Matrix Inversion B) Determinants C) Both A and B
C) Both A and B
Fill in the blank: The characteristic polynomial of a matrix is used to find its ____.
eigenvalues
What is an eigenvector?
An eigenvector is a non-zero vector that changes at most by a scalar factor when a linear transformation is applied.
True or False: The eigenvalues of a matrix can be complex numbers.
True
What is the purpose of matrix decomposition in structural engineering?
Matrix decomposition simplifies complex matrices into simpler components for easier computation.
Multiple Choice: Which method is commonly used for solving large systems of equations in structural analysis? A) Gaussian Elimination B) Matrix Inversion C) Both A and B
A) Gaussian Elimination
What does the stiffness matrix represent in structural engineering?
The stiffness matrix relates the displacements of a structure to the forces applied to it.
Fill in the blank: In matrix notation, the equation F = kx represents ____.
force equals stiffness times displacement
What is the role of the global stiffness matrix in structural analysis?
The global stiffness matrix combines the stiffness matrices of individual elements to analyze the entire structure.
True or False: The global stiffness matrix is always symmetric.
True
