The following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?

Q: Let u = 4i + 5j, v = -4i +2j, and w = 3i - j. Determine the i, j form of each of the following: (a)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: This problem is from Linear Algebra. It's based on Module 2. The book is called Linear Algebra Math…

A: The problem concerns convex linear combinations of vectors

Q: = Let -3 -1 -~--~--~--~--~- , V3 -5 1 , V₂ 2 0 combination of V₁, V2 and V3. 5 -26 , V4 -9 -1 -3…

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Q: Because [-37-2]] + [-27-5j]= and The [-21-5j] + [-3i-2j] = we can conclude that vector addition is +…

A: The solution is mentioned below.

Q: skip the first 3 thank you

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Q: 3. Solve the system below using the specified method. Write your answer in vector form. X1 - 3x2 = 2…

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Q: -14 Given that write 3 -5 -3 -14 ] -5 = 2 -2 -3 1 0 0 −1 −1 as a linear combination of the vectors 1…

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Q: Solve the system below using the specified method. Write your answer in vector form. X1 - 3x2 = 2…

A: I have written in the form Ax=b and used inverse matrix method.

Q: 2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your…

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Q: For what values of h are the vectors 1 1 1 2 2 h+1 linearly dependent? 1 3 4 h+2 " and h = −1 and h…

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Q: how that vectors[ A-2i+ 3j - 2k,B=I +2j+ 4k ] are perpendicular to each o

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Q: response. Justlfy_your ans 1 1 -1 is a linear combination of the vectors y, 2 Show whether or not…

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Q: Let A = 1 3 -3 0 V1 = 2. Find a basis for Nul(A)+. 0-2 A basis is {v₁, v₂} where V2 ||

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Q: The vectors listed in Eq. (10) are used in several of the exercises that follow. VI = [2]· 2 -[3].…

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Q: Solve the following vector equation:

A: Introduction: The graph of a system of two equations in two variables (x and y) is a pair of lines…

Q: Let v1 = (-6, -6, -9), i2 = (3, 3, 12), iz =(-1,-1,6). Are the vectors v1, 02 and vz linearly…

A: See the attachment

Q: 6. Prove that A ·B+ |A x B|< 2|A||B|| for arbitrary vectors A, B and C.

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Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: 98. Determine whether the vectors AB and PQ are B(-2, 2, 0), where A(1, 4, 1), equivalent, P(2, 5,…

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Q: Do question 10 only

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Q: 1 4 Give a reason why the vectors 1 are 8 -88 arly dependent. (3 pts) Write one vector as a linear…

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Q: Determine whether v = 3i - 5j and w = 6i - 10j are parallel,orthogonal, or neither.

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Q: Linear algebra: please do q7, 9, 11 correctly and handwritten. Equ 6 is Vx= 0

A: We have to determine whether the given set is linearly independent or dependent

Q: For what values of h are the vectors 3 100-W and 4 h h+1 2h+3 linearly dependent? O 2 2 h can be any…

A: To determine the value of  for which the following vectors are linearly dependent.

Q: That is not correct. The first Vector answer is [-2/3, -1/3, -2/3] (column wise format.)

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Q: 2. Let A = a₁ + a2j + a3k and B = b₁i + b₂j + b3k. Then (A × B) . j is equal to a) a2bვ — a3b2 b)…

A: A=a1i+a2j+a3k B=b1i+b2j+b3k.

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given,S = { (2, -1, 3), (5, 0, 4) }To find:  the vector as a linear combination of the vectors in S.…

Q: a = (3, 2, 4), b = (-3, 3, 0), c = (0, 0, -2) %3D (a) Find a x (b x c). a x (b x c) = || %3D (b)…

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Q: Let a₁ = , a₂ = [2] and b = -7° -13 -8 s b a linear combination of a₁ and a₂? OA. b is not a linear…

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Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

Q: Why vector of algebra related in maritime industry

A: Vectors are mathematical objects that have both magnitude (size) and direction. In the maritime…

Q: (a) Express the vector a × b in the form aa + 3b + yc, assuming that the vectors a, b and c are not…

A: a)  Look care fully that we need to find the coefficients   namely α,β,γ   Determination of α:…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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