What is the concept of matrices and how are they manipulated?

Hey ! What do you mean by manipulation ? At their very basic levels, matrices are just a way to arrange numbers / symbols / whatever mathematical expression you want into a grid. You can assign meaning to different lines or columns, which can help with more complex problems. In terms of basic operations, you can sum them and substract them as you would anything else (corresponding cases sum up together). For multiplication, it's best explained using an example. Let's say you want to multiply a matrix A with 2 rows and 3 columns with a matrix B with 3 rows and 2 columns. The result CC is a matrix with 2 rows and 2 columns. The first result in C (1st row, 1st column) is the sum of each element in the first row of A multiplied by the each element in the first column of B. So it'd be A_row_1 * B _column_1 + A_row_2 * B_column_2 + A_row_3*B_column_3. Does this make sense ? In some cases, these manipulations are enough to use matrices to solve systems of equations. You can't divide by a matrix, but you can divide by its inverse. Calculating the inverse of a matrix is a bit more complicated, as you need to get into determinants, etc, but for each step that's a little bit harder, you can start doing a lot more new things with them. I'm not sure I've fully answered your question, so let me know if there's anything else or more specific you want to know :)