Questions and answers on matrices
Q: What is a matrix?
A: A matrix is a two-dimensional array of numbers, arranged in rows and columns.
Q: What is the size of a matrix?
A: The size of a matrix is determined by the number of rows and columns it has. For example, a matrix with 3 rows and 4 columns is called a 3x4 matrix.
Q: What is the order of a matrix?
A: The order of a matrix is the same as its size, represented as (rows x columns). For example, the order of a 3x4 matrix is 3x4.
Q: What is a square matrix?
A: A square matrix is a matrix that has an equal number of rows and columns. For example, a 3x3 matrix is a square matrix.
Q: What is the transpose of a matrix?
A: The transpose of a matrix is obtained by flipping the matrix over its main diagonal, i.e., interchanging rows with columns.
Q: How do you add two matrices?
A: To add two matrices, their sizes must be the same. You simply add the corresponding elements in each matrix to get the resulting matrix.
Q: How do you multiply two matrices?
A: To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
Q: What is the identity matrix?
A: The identity matrix is a square matrix that has 1s on its main diagonal from top-left to bottom-right, and 0s elsewhere.
Q: What is an inverse matrix?
A: An inverse matrix is the matrix which, when multiplied by a given matrix, gives the identity matrix. It only exists for square matrices that are invertible.
Q: How do you find the determinant of a matrix?
A: The determinant of a square matrix is a scalar value calculated from its elements. There are various methods to find the determinant, such as expansion by minors or using properties like row operations.
Q: What is the rank of a matrix?
A: The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It provides a measure of the matrix's "fullness" or dimensionality.
Q: What is eigenvalue and eigenvector of a matrix?
A: An eigenvector is a non-zero vector that, when multiplied by a matrix, only changes in scale but not in direction. The corresponding eigenvalue is the scalar that scales the eigenvector. They play an important role in various mathematical and engineering applications.