-2t Question : Let H be the set of all vectors of the form 5t Find a 3t vector v € R3 such that H = Span{v}. Why does this show that H is a subsnace of R3

Q: Find the magnitude of vector v. 1 X + + 1 2 4 (4,-3) -2+ -3+ -4 -5 - ليا 3 5

A: To find the magnitude of the given vector v .

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: Let v = [2 10. (a) How many vectors does Span {v} contain? (b) List a few vectors in Span {v} and…

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Q: Find all values of a such that the vectors = and are perpendicular

A: Given:The vectors are  and  are perpendicular.To Find:The value of .Concept Used:When two vectors…

Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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Q: Q3) A) Let 4 (-1 3, 4) and B (-5, 8, 10) two points in the space, find: 1- The vector AB. 2- Length…

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Q: 5. Let S = {V₁, V2,..., Un}, n ≥ 2 be a set of nonzero vectors of V. Each of the following…

A: Given,  S= { v1 , v2 , v3 , ...... ,vn } , n>=2 is a set of nonzero vectors of V .

Q: Can a vector in a vector space R -4 - 2 be 2. span by -1 2 イ

A: Span of vectors.

Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: If some p vectors can span V, then dim V= p True False

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Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

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Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Suppose u, v and w are non-zero vectors in R" such that proj(-2v) a and proj(5w)= b. Use the…

A: Projection vector of a→ in the direction of b→ Proj b→a→= a→.b→b→×b^=a→.b→b→b→2

Q: Let v1 = v2 = 3 v3 = Are the vectors v1, v2 and vz linearly independent? linearly dependent If the…

A: Vectors v1, v2, v3 are linearly dependent if C1v1+c2v2+c3v3 =0 implies atleast one Ci is non…

Q: A vector in three dimensions can be written in either of two forms: in coordinate form as v = (a₁,…

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Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

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Q: Find the length of the vector v = (9, 3, 9). ||v|

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Q: Suppose V1, V2, V3, V4, V5 are distinct, nonzero vectors in R³ = and suppose that span(V1, V2, V3,…

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Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Determine whether or not the following set of vectors span R³, (i) {(1, 1, 2), (1, -1, 2), (1, 0,…

A: Span of R3 .

Q: If V1 = [1 4 0] and V2 = [ -2 0 8], then determine all possible 1x3 row vectors V3 such that the set…

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Q: Q3 O Let w-l(a,b,c), b= 3a} is Sub Sehoof RE a Sub Spaceef R32 is s w X, = i +2j - K , Xz= -3i+2j-R…

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Q: The vector -3 (GIE) -1 -4 0 -7 vectors -3 2 belongs to the span of the 5 Select one: O True O False

A: Given: W=span-3-10, -1-4-7. To check v=-325∈W.

Q: Find a vector orthogonal to all vectors in the set ((2,1,2), (2, – 2,3)) . Write your answer as an…

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Q: Determine whether the vectors ?→ = (2,−1,3), ? → = (1,1,−2), and ? → = (3,−1,5) span ℝ?. If not find…

A: Span: Let us consider the set of  vectors S={v1,v2,v3,......vn} in a vector space V is said to be…

Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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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.