Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Look at the given matrix J, which is [[1, 1], [1, 1]]. This means it has 2 rows and 2 columns.
Step 3: Identify the rows of the matrix. The first row is [1, 1] and the second row is also [1, 1].
Step 4: Determine if the rows are linearly independent or dependent. Two rows are linearly dependent if one row can be formed by multiplying the other row by a constant. Here, both rows are identical.
Step 5: Since both rows are the same, they do not add any new information. Therefore, they are linearly dependent.
Step 6: The rank of a matrix is the number of linearly independent rows (or columns). In this case, there is only 1 linearly independent row.
Step 7: Conclude that the rank of matrix J is 1.
Matrix Rank – The rank of a matrix is the dimension of the vector space generated by its rows or columns, indicating the maximum number of linearly independent row or column vectors.
Linear Dependence – Rows or columns are linearly dependent if at least one row or column can be expressed as a linear combination of others.
