Consider the 2 X 2 matrices A1 =  1      1           A2 =  0      1        A3  =   0      0      A4  =  1      0           0      0                    0      1                    1      1                1      0 (i) Argue whether these four matrices are linearly independent or not in the vector space of 2 X 2 real matrices. (ii) Find the dimension of span(A1, A2, A3, A4).

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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.