2. Let {v1, v2, V3}, {w1, w2, w3} be two sets of linearly independent vectors in R³. (1) Show th it there exists a 3 × 3 matrix A such that Avı =w1, Av2 =w2, Av3 =w3. (2) Let B be any 3 x 3 matrix such that Bvi =w1, Bv2 =w2, Bv3 =w3. Show that A = B. In other words, the matrix A constructed in (1) is unique.

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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.