Sure, the dimension of a matrix is defined by the number of rows and columns it has.
Step 1: Count the number of rows
To determine the number of rows in the matrix, we simply count how many individual lists there are within the main list. Each list represents a row. The matrix provided has 4 individual lists, so it has 4 rows.
We get the following rows:
1. [1, -5, 0, 0, 0, -3]
2. [1, 4, -2, 4, -5, 3]
3. [1, -3, 4, 0, 1, 0]
4. [-2, -5, -2, 5, 0, -1]
Step 2: Count the number of columns
We can determine the number of columns by looking at how many elements there are within an individual row. Each element in a row corresponds to a column. Looking at the first row, there are 6 elements. Therefore, we have 6 columns.
Step 3: Define the matrix dimensions
We have determined that there are 4 rows and 6 columns in this matrix. So, we could say that the dimension of this particular matrix is 4 by 6, often written as 4x6.
Therefore, the matrix [[1,-5,0,0,0,-3],[1,4,-2,4,-5,3],[1,-3,4,0,1,0],[-2,-5,-2,5,0,-1]] is of dimension 4x6.