Step 1: Identify the matrix F, which is given as F = [[1, 2], [2, 4]].
Step 2: Look at the rows of the matrix. The first row is [1, 2] and the second row is [2, 4].
Step 3: Check if the second row is a multiple of the first row. To do this, see if you can multiply the first row by a number to get the second row.
Step 4: Notice that if you multiply the first row [1, 2] by 2, you get [2, 4], which is exactly the second row.
Step 5: Since the second row is a multiple of the first row, it does not add any new information. This means there is only one linearly independent row.
Step 6: The rank of a matrix is the number of linearly independent rows. Since we have found only one linearly independent row, the rank of F is 1.
Matrix Rank – The rank of a matrix is the maximum number of linearly independent row or column vectors in the matrix.
Linear Independence – A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others.
