Let A be a 3 × 5 matrix. (a) Give all possible values for the rank of A. (b) If the rank of A is 3, what is the dimension of its column space? (c) If the rank of A is 3, what is the dimension of the solution space of the homogeneous system Ax = 0?

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.