Determine whether the vector U = 2 is a linear combination of the vectors Xi = 2 X2 = and X ? Give reason(s) for your response.

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

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Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

Q: Express the vector in terms of the unit vectors i and j. 2(3, 3) + 3(4, 2)

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: C A

A: We use Triangle law

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

A:

Q: Find the unit vector u in the direction of the vectorv=(-5, 12, 0).

A: Given          v =( -5, 12, 0 )

Q: Find the unit vector in the same direction as the vector u = [8, –7].

A: When you divide a vector by its magnitude you get an unit vector along its direction.

Q: What is the zero vector?

A: We have to define

Q: Find two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: How do you determine if two vectors are orthogonal?

A: If we are given two different vectors , then they are orthogonal if they are  perpendicular to each…

Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

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Q: Q2) A- Use two methods to create the vector x having 100 regularly spaced values starting at 5 and…

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Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Find two linearly independent vectors perpendicular to the vector V = 3 -5

A: Let's find.

Q: Find two linearly independent vectors perpendicular to the vector 4 v =

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Q: how can i learnd about vector in r2 and r3?

A:

Q: B)Find value of h for which the vectors are linearly independent, justify answer

A: 2-24 , 4-67 ,-22h

Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: 9. Explain why four vectors is R³ are always linearly dependent.

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Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

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Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

Q: Which two vectors are perpendicular to both å and b?

A: result of vector cross product of two vector is perpendicular to both the vectors.

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: Determine if the given vectors are linearly independent or linearly dependent.

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Q: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

Q: Calculate and display the error vector & and use it (c) to provide an orthogonality check on your…

A: Given: The set of data points, x y z 0 0 4 1 0 4 0 1 4 1 1 0 To plot them on a set of…

Q: What helps to set of vectors linearly independent?

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Q: Write the vector v= 1 as the linear combination of vectors --0 w =

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Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Q:: Determine whether the vector w= is a linear combination of the vector u= and the vector v = ?

A: w is not a linear combination of vector u and the vector v.

Q: Find a non-zero vector perpendicular to the vectors -2 and ü = 2 ||

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Q: Find self-value and self-vectors.

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Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry

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.