LINEAR EQUATIONS

Creating a Matrix Substituting Within a Symbolic Matrix Manipulating Regular Matrices Vectors Scalar Multiplication Addition of Matrices Gauss-Jordan Elimination Reduced Row-Echelon Form Dot Product Rank Number of Solutions

Vectors How to Examples Exercise How to: Vectors are simply a special type of matrix that have only one row (1xN) or one column (Nx1). Creating a vector is no different than creating a regular matrix:      rV = [Row vector entries etc.] or      cV = [Column; vector; entries; etc.] But, we can also separate a row or column vector from a matrix by utilizing the colon operator:      rV = A(i, :) (the i-th row of matrix A) or      cV = A(:, j) (the j-th column of matrix A) Examples: Let's create 2 vectors, one a row vector and one a column vector, whose entries are 1, 2, and 3. For the row vector we have:      rV = [1 2 3] And for the column vector:      cV = [1; 2; 3] Now, let's create the same vectors, but this time by copying them from the matrix, R, with 10, 1, 13 in the first row, 1, 2, 3 in the second row, and 9, 3, 11 in the third row. You can see that the second row has 1, 2, 3 just like we want:      rV = R(2, :) Also, reading down the second column, we see 1, 2, 3 in order as well:      cV = R(:, 2) Exercise: Given a matrix A = [4 7 8; 0 0 3; 8 7 9], extract from it a column vector with values 8, 3, 9. Click here to see the answer.