Let s= {(1,3.5). (3. 3, 2). (-1, 1.8)} be a basis for R. If u = (8, 8, 1), then (u), - A) (1 2 1 B) 2 21 C) |1.2 -1 D) |2. 1. 1||

Q: Explain why S is not a basis for M2,2.

A: Let's check if S is linearly independent or not. S will not be linearly independent if for some…

Q: Let Is S a basis for R³?

A:

Q: Determine whether the set {v1, v2} is a basis for R2.

A: Basis:     "If V is any vector space and U=u1, u2, . . . , un is a finite set of vectors in V,…

Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: Prove i = [- 2,5, 1], = [2,1, – 1] and w = [-6,0, – 12] are orthogonal. %3D %3D %3D

A: SEE ATTACHMENTS

Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Iif a basis for g2is y3 = { 4 and : 7 2 find the coordinate vector [X] -5 5 3

A:

Q: | Let v₁ = (1, −1, 1, − 2), v₂ − (−1, 2, −1, 1), v, −(−2, 1, −1, 5). Determine whether {V₁, V₂, V3}…

A:

Q: - Determine if S = {[1246]} 0 forms a basis for M2,2.

A: We know that M2×2 is a vector space of all 2×2 real matrices over R.Given that .We need to determine…

Q: 2

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Q: The set B = {1+t², t + t², 1 + 2t + t²} is a basis for P₂. Find the coordinate vector of p(t) = 1 +…

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Q: Which of the following is a basis for R? O a. {(1,0), (2,0)} O b. (1,2), (2,3), (1,7)} O c.…

A: We have to check

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: 2. Determine if the set is a basis of R3 [t] . {t² + 2t -3, t² + 5t, 2t² — 4}

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Q: 2 3 [+0 4 2 b = -2 Select true or false for each statement. Let A = and c = [12] 1. The vector c is…

A: The objective of the question is to determine whether the given vectors b and c are in the kernel…

Q: Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c)…

A: The following are the rules in the Einstein's summation convention having the index notation:1) The…

Q: 16. Determine whether the given set forms a basis for P3. {-1 -r', 2r + 2r", –2r + r – a*, 1+ r² +…

A: Follow the steps.

Q: Consider following five sets: 1. { , } { } II. { } III. IV. { , , } V. { , } Find all set(s)…

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Q: The set S = {(1, 1, 0), (-2, 4, 1), (3, 2, -5), (-1, 3, -2)} is: Select one: a. Dependent. O b.…

A:

Q: 9. Let S = { (1,2), (4, 5), (0, 2)}. Check whether S is a basis for ?2?

A:

Q: Which of the following are bases of R3? {(1, 0, 0), (1, 1, 1), (2, 1, 3), (1, 1, 1)}; {(1, 0, 0),…

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Q: Let A = - 7 -6, b 3 2 = [4].. and c = Select true or false for each statement. [1] 1. The vector c…

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Q: 9. Given B = { (3,0,-3), (3,-2,1), (-1, -6,1)} and B' = {(1,1,–1),(0,1,2),(-1,1,0)}, find the…

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

A:

Q: 0,1,0) R3 Ba

A:

Q: Determine whether each of the sets below is a basis for R³. Explain any theorems or results you rely…

A: NOTE: Refresh your page if you can't see any equations. . write all 3 vectors in the matrix the…

Q: REMOVE vectors from Ac (P,[R], +,). To obtain a BASE for (P.[R],+,): of the items 25 and 26 (Item…

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Q: Which of the following sets of vectors is a basis for R?? {[:]}. 2 3.

A:

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 =…

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

A: 5) Given  that  Let, So we have  .Hence Noted that .Because  Hence basis for subspace V of  is

Q: 4. Consider f(x) = sinr. If f(x) is interpolated by p2(2) polynomial with the nodes {-7.0, }, the…

A:

Q: 6. Can any of the given sets of 3-vectors below span the 3-space? Why or why not? (a) [1 2 1] [231]…

A: We have to check whether the given set of 3-vectors span the 3 space. (a) 1 2 1, 2 3 1, 3 4 2 (b) 8…

Q: 9. Determine whether the set of vectors i (2,-1), (3,-2), (0, 1)} basis for TR? is

A: We will check whether the given set of vectors is a basis of R2 or not.

Q: 7. Let B = {(1,2,3), (2,0, 4), (1, 1, 1)}. Prove that B is a basis for R³ (since this is a proof,…

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Q: 1 Q.2) How can you show that the set{ 2 2} form basis of xy- plane in R3? 3

A: GIVEN SETS : The given sets are : 120,123 The augmented matrix is : 120123R2→R2-R1~120003

Q: Let i = (6, – 6, 1) and v = (– 5, 5, – 6). %3D Compute the following: i · i = i. i = - 6(ü - i) = (–…

A: To evaluate the given dot product of vectors u and v.

Q: -10000) Say for what values of a and b the set A is a basis of R4 Consider the set

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Q: 1 If T is defined by T(x) = Ax, find a vector x whose image under Tis b, and determine whetherx is…

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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.