23 Linear Transformations and Matrix Algebra 2 (g) (x e R : x =s for some s, te R} 1 +t 2 3 2 (h) (x e R3 x= LJ for some s,te R} +S 0 t 2 1 2 2 1 (i) {xe R3 for some s, t e R} +s :X = 4 +1 2 1 -1 -1 2 Criticize the following argument: By Exercise 1.1.13, for any vector v, we have Ov 0. So the first criterion for subspaces is, in fact, a consequence of the second criterion and could therefore be omitted. #3. Suppose x, V1,. Vk E R" and x is orthogonal to each of the vectors v1, ... , Vk. Prove that x is NO

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A:

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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.