Multiplication by a Scalar
If we have a matrix A = \([ [2,4], [6,8] ]\), what is the result of multiplying matrix A by the scalar 3?
Multiplication
Multiply the following matrices: \( A = \begin{bmatrix} 3 & 4 \\ 2 & 1 \\ 5 & 6 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \)
Subtraction
Let's consider two matrices A and B. Matrix A is a 2x2 matrix with the elements \([2, 5; 3, 4]\) and Matrix B is a 2x2 matrix with the elements \([1, 3; 2, 2]\). What is the result of the operation A - B?
Finding the Identity Matrix
Find the identity matrix for the 2x2 matrix A = \[\begin{pmatrix} 4 & 3 \\ 2 & 1 \end{pmatrix}\]
Finding the Scalar multiplied by the Identity Matrix
What is the result of the scalar 5 multiplied by the 3x3 identity matrix?
Addition
Given the matrices A = \(\begin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix}\) and B = \(\begin{bmatrix} 5 & 7 \ 6 & 8 \end{bmatrix}\), find the result of the operation A + B.
Simplifying the Matrix Operation
Given the matrices A = \( \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{bmatrix} \) and B = \( \begin{bmatrix} 3 & 2 & 1 \\ 6 & 5 & 4 \\ 9 & 8 & 7 \\ \end{bmatrix} \). Find the result of the operation 2A + 3B.
Finding the Determinant of a 2x2 Matrix
Find the determinant of the 2x2 matrix \(A = \begin{pmatrix} 3 & 4 \\ 5 & 6 \end{pmatrix}\).
Finding the Determinant of a 3x3 Matrix
Find the determinant of the following 3x3 matrix: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]
Finding the Determinant of Large Matrices
Find the determinant of the matrix \( A = \begin{bmatrix} 3 & 0 & -1 & 4 \ 1 & 5 & 0 & -2 \ 4 & 1 & 2 & 1 \ 2 & 0 & -1 & 3 \end{bmatrix} \)
Inverse of a 2x2 Matrix
Given the matrix A = \(\begin{bmatrix} 3 & 4 \\ 2 & 5 \end{bmatrix}\), find the inverse of A.
Inverse of an nxn Matrix
Find the inverse of the matrix \(A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 1 & 0 & 1 \end{bmatrix} \).
Finding Reduced Row Echelon Form
Find the reduced row echelon form of the matrix \(A = \begin{bmatrix} 1 & 2 & -1 \ 2 & 4 & -1 \ 3 & 6 & -3 \end{bmatrix}\)
Finding the Transpose
Given the following matrix, \[A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\], find the transpose of matrix A.
Finding the Adjoint
Find the adjoint of the matrix \( A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{bmatrix} \)
Finding the Basis and Dimension for the Column Space of the Matrix
Given a matrix A = \(\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}\), find the basis and dimension for the column space of the matrix.
Finding the Basis and Dimension for the Row Space of the Matrix
Find the basis and dimension for the row space of the following matrix: \[\begin{pmatrix} 1 & 2 & 3 \ 2 & 4 & 6 \ 3 & 6 & 9 \end{pmatrix}\]
Finding the LU Decomposition of a Matrix
Find the LU Decomposition of the following matrix: \[ A = \begin{pmatrix} 2 & 3 \cr 5 & 7 \end{pmatrix} \]