Elementary Row Operations

Key Questions

• What is a matrix transpose?

  The transpose of a matrix is found by creating new matrix where the rows and columns are swapped out. If i denotes row and j denotes column, we have `a_(ij)` becomes `a_(ji)`.

  Suppose you have a matrix A. The transpose is denoted `A^T`. Let us take a 2 x 2 matrix for simplicity.

  `a_(11)` is row 1, column 1. The transposed entry would stay the in the same place.

  `a_(12)` is row 1, column 2. The transposed entry would be placed in Row 2, Column 1`a_(21)`.

  `a_(21)` is row 2, column 1. The transposed entry would be placed in Row 1, Column 2`a_(12)`.

  `a_(22)` is row 2, column 2. The transposed entry would stay in the same place.

  Matrix Transpose Calculator

  Don S. · 4 · Aug 19 2014
• What are the elementary row operations of matrices?

  There are three elementary row operatins of matrices:

  • Exchange two rows position;

  • Substitute a row for the sum of it and another row;

  • Multiply a row for a scalar;

  Hop it helps.

  Bernardo Russo G. Ferreira · · Oct 14 2014

• What are eigenvalues?
• Do elementary row operations change eigenvalues?
• What are the elementary row operations of matrices?
• What is a matrix transpose?
• How do I perform matrix multiplication?
• How do I find the eigenvalues of a `2xx2` matrix?
• How do you find the `LU` factorization for `tildeA = [(1,0),(-3,1)]` such that `tildeL` is unit diagonal?
• How do you factor `((1, 2, -3), (0, 1, 3), (0, 0, 1))` into a product of elementary matrices?
• How do you perform the row operation `R_2-> R_3` given `[(4,-1,6,-8), (2,4,7,3), (8,1,-9,-2)]`?
• Find the matrix A (in terms of B, C, and D)?