2. Let vị = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, V2, V3} is a basis for R³. Also, let T: R³ → R² be the linear map for which %3D %3D T(v1) = (1,0),T(v2) = (-1,1),T(v3) = (0,1). Then find T(7,13,7).

Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

A:

Q: 5. Let ū = (0,2, 1), ở = (-1,0, 2) and w = (2,3,0). Find the coordinates of (2,2,2) with respect to…

A: This question is related to vector space. Solve in 2nd step .

Q: Determine if the following set of vectors is LD or LI. If LI explain how you know (explain your…

A: Here, 3 vectors are: {(1,2,3),(4,5,6),(2,1,0)}

Q: Consider a linear map T: U → R² and uí, u₂ € U. Given that T (u) = (-3,6) and T ԱՉ mapped to (0, 0)…

A: Given: Tu1→=-3,6T ; Tu2→=5,-10T.We need to find the vector which is mapped to 0,0T.

Q: The vectors ₁ = (2, -3,1), u₂ (1,4,-2), uz = (-8, 12, -4), U4 = (1,37,-17), and u5 = (-3, -5, 8)…

A: We are given five vectors in R3. Out of these we have to find a subset that form the basis of R3.the…

Q: Evaluate e fry²dæ + x³dy, where C' is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2)

A: We apply the green's theorem to solve the given problem.

Q: into M2, such that M2,2 Let T be a linear transformation from (::)-[: (::)-[ 0 1 0 2 1 2 0 1 1 0 1 3…

A: Solution

Q: Let S = { (0,0), (0,3), (1,0), (1,2), (2,0), (3,2) } Find S', the transitive closure of S

A:

Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

A:

Q: R* Basis ? Is t Ś (l,D,0,1),(0,1.0,0).(1,1,1.2).(0,1,1,1)3

A:

Q: Show the span {(1,0, 1), (-1, 2, 3), (0, 1, – 1)} is all of R'.

A: Let x=1, 0, 1, y=-1, 2, 3 and z=0, 1, -1. We have to show that spanx, y, z is actually the vector…

Q: {₁,...,} is linearly independent if and only if {₁,...,} is an orthogonal set. True False

A:

Q: if u = <1,-3,1> and v = <2,2,2> then find the projection of u onto v

A: The objective of this question is to find the projection of vector u onto vector v. The projection…

Q: 6. Let T: R³ → R² be given by 74-7 8-6.5.) = T Show that I is a linear transformation by confirming…

A:

Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

A:

Q: Question 2: For which real values of a do the polynomials P1(t) = at? -t-; P2(t) = - + at -; P3(t) =…

A:

Q: 7.4Find a subset of the vectors v= (1, -2, 1, -1), v2= (0, 1, 2, –1), vz= (0, 1, 2, –1) and v,= (0,…

A:

Q: Let a = (0, 3, 5) and 6 = (0, 1, 4). Find the projection of b onto a. proja b V - λ

A: Given:        a→=0,3,-5         b→=0,1,4 The projection of b→ onto a→ is:…

Q: 15. Let x = (x1, x2). Using the feature mapping show that *(2,3)·¤((4,4) –-(2,3)·(4,4)*

A: Given that for x=x1,x2, the feature mapping is…

Q: {(1, 2; 3 ), ii) {(1, 1, 1). (0, 1, 1). (0, 1, –1)}. 0. 1). (2, 1, 3)} spar

A:

Q: Suppose ū (5, 3, 0) and v = (3, 1, –1). The projection of ū along ở is

A:

Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1,0,0)T., (2,0, 1,0), and (0, 0, 0, 1) form a…

A: The given set is .Now

Q: Let a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

A:

Q: Let à = (1, 1, 4) and b = (1, 2, - 5). of b onto a. - Find the projection proj- 6 = b =< -

A: For the given vectors the projection of b on a is given by

Q: and the projection pros

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Q: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows R = {(0, 1), (1,1), (2,…

A: The given sets are -…

Q: Let →a=⟨−4,1,−2⟩a→=⟨-4,1,-2⟩ and →b=⟨−2,−3,4⟩b→=⟨-2,-3,4⟩. Find the projection of →bb→ onto →aa→.…

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.