Question 3: a) Check whether the following is the subspace of R3 or not ? (step by step answer) W = {(x,y,z), x² + y² + z² < 1} Question 4: a) Determine k so that the vectors (1, –1, k – 1), (2, k, –4) and (0,2 + k,-8) in R³ are linearly independent. b) Let V be the real vector space of all function defined on R into R. Determined whether the given vectors are linearly independent or linearly dependent {x, cos x}.

Q: 4. State with a brief explanation whether the following statements are true or false. (a) The…

A: a) true The vectors (1 ,0) and (0,1) is linearly independent. We know that linearly independent set…

Q: QI. Show that the vectors x, =(1,2,4), x, = (2,-1,3), x, (0,1,2) and x, =(-3,7,2) are linearly…

A:

Q: Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each…

A:

Q: (i) Let {u, v} be linearly independent vectors in a vector space V. Determine whether set {v – u, v…

A: 7 (i) Given, u, v be linearly independent vectors in a vector space.

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

A:

Q: Prove that the vectors (1,1,0),(3,1,3) and (5,3,3)  are linearly dependent

A:

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.