Rank (A) =2 means..? In a 4*4 matrix
Answers
Answer:
Step-by-step explanation:
The maximum number of linearly independent rows in a matrix A is called the row rank of A, and the maximum number of linarly independent columns in A is called the column rank of A. If A is an m by n matrix, that is, if A has m rows and n columns, then it is obvious that
What is not so obvious, however, is that for any matrix A,
the row rank of A = the column rank of A
Because of this fact, there is no reason to distinguish between row rank and column rank; the common value is simply called the rank of the matrix. Therefore, if A is m x n, it follows from the inequalities in (*) that
where min( m, n) denotes the smaller of the two numbers m and n (or their common value if m = n). For example, the rank of a 3 x 5 matrix can be no more than 3, and the rank of a 4 x 2 matrix can be no more than 2. A 3 x 5 matrix,
can be thought of as composed of three 5‐vectors (the rows) or five 3‐vectors (the columns). Although three 5‐vectors could be linearly independent, it is not possible to have five 3‐vectors that are independent. Any collection of more than three 3‐vectors is automatically dependent. Thus, the column rank—and therefore the rank—of such a matrix can be no greater than 3. So, if A is a 3 x 5 matrix, this argument shows that