Verify that this is a vector set check each property(assoctive, etc): X = (x0, x#) Y = (yo, y#) X+Y (xo + yo, x# +_y#) scalar × X = X = (sclar × x0, sclar × x#)

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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Q: Verify that this is a vector set check each property(assoctive, etc): Y = (yo, y#) (xo + yo + 1, x#…

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Q: Explain how vectors written in component form are added or subtracted.

A: Vectors written in component form can be added by adding the corresponding components of both the…

Q: Let 2 = (-8,1) and To (-7, -2) Compute the following vector B Prijz To projections.

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Q: Find a subset ofbthebvectors v1=(0,2,2,4), v2=(1,0,−1,−3), v3=(2,3,1,1) and v4=(−2,1,3,2)that forms…

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Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: How are a vector and a scalar different?

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Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

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Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

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Q: How do you know if 3 vectors span R^3? Is there any example?

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Q: Find a vector orthogonal to both and . Include a step by step solution please

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Q: We know that there are two ways to multiply vectors: the vector and scalar product. How about vector…

A: Vector division is not possible .

Q: Define how to combine vectors using matrices.

A: To Explain: how can we combine vectors using matrices.

Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: x1-3x2 = 1 -8x1-7x2= 1 3x1+2x2 = 4 -10x1-x2 = -2 You can resize a matrix (when appropriate) by…

A: Answer given below.

Q: what if it was the same vector, but 5y^2j?

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Q: Describe all of the operations involved in (a - b)(a c) — 2ã · (b × c) - Explain whether the final…

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Q: Let vi = (-9,9, 6). v2 = (2, 6, 4). v3 = (4,0,0) in Rº. Find a nontrivial linear relation among…

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Q: find a vector that is orthogonal to (1,2,3) and (4,5,6). do not use cross product.

A: Let's find vector that is orthogonal to given two vectors.

Q: Describe all solutions of Ax = 0 in a vector form, where -4 -2 0 3 2 0 0 0 1 1 A = -1 -4

A: Here given matrix is

Q: Write out the expressions a- Va in index notation for vector a

A: Let us consider a vectora→ = a1i^ +a2j^ +a3k^where a1 , a2, a3 are functions of (x1, x2 & x3)and…

Q: Obtain Vector v = 3î+ 4ftransformed with -1 1 3 2 –4]

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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: When multiplying a scalar and a vector: |ha|=|ā| when A |xa|=|||ā| when > + 0 and + 0.

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Q: Write the interpretation of independent vectors, span, basis and dimension. Take the example of…

A: We have to give the interpretation of independent vectors, span, basis and dimension by taking the…

Q: The scalar multiplication of a vector by a positive value results in another vector having the same…

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Q: Orthonormalize the following set of three vectors: {(1, -1, 2), (1, 3, 1), (1, 0, 2)}. Please use…

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Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: (1) S={(2,-1,3), (5,0,4)} (a) u=(1,1,-1) (b) w=(1,-8,12)

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Q: Vector u has POSITIVE x-component, POSITIVE y-component and ZERO z-component. Vector v has NEGATIVE…

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