3. Find the gradient of U = 4xz² + 3yz. А. 4z3а, + 3za, + (8xz + Зу)а, В. 4z? а, + 3zay + (8xz + Зу)а, С. 4za, + Зyza, + (8xz + Зу)а, D. 4z7ax + 3yzay + (8xz + Зу)а,

Q: (b) ||ū× w|| (u • w) (c) (d) (r+s) ux v + w s(v+w• w) × (rv)

A:

Q: Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

A: We have to find the scalar product a·b when (i). a=x+2y-z and b=2x+3y+z(ii). a=x-3y+z and b=2x+y+z

Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

A:

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A: Given that,

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A: The given vectors are v→=x1x2x3 and w→=y1y2y3.

Q: 1.28 Vector concepts: Solving a vector equation? (Section 2.9.3) Shown right is a vector equation…

A:

Q: 1. Given the vectors U = i- 2j+k, V = 2i+j+k and W = 3i – j+ 2k, compute the following: U (c) ||U||

A: The solution is :

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A: We have to find out whether the given statement is true or false according to the given appendix.

Q: Linear Algebra: Explain the term "Vector basis" giving example to support your answer.

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Q: Y1 Let v = and w = Y2 be vectors in R. Compute the following. y3 Preview Preview Preview Note: Enter…

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Q: (5) True/False The set of continuous functions f defined on the interval [0, 1] such that f(0) = 1,…

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A:

Q: Use the function to find the image of v and the preimage of w. T(v,, v2) = v, - V2, V1 + V2, 2v, -…

A:

Q: 4. A quadratic form Q in the components ₁,...,n of a vector = [₁,...,n] with symmetric coefficient…

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Q: True or False? If two vectors are linearly dependent, then each is a multiple of the other. True…

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Q: Linear Algebra  find a representative of x (vector)

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Q: Use matrices to stretch the vector horizontally by a factor of 3. O O O O

A:

Q: 8. Find the value of a if F = (axy-z)i+(x+2 yz) j+(y - axz)k is irrotational. %3D

A:

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Q: 6. Perform the following computations (a) Compute (2, 0, 3) × ((1, 1, 1) + (4, 0, 6)). (b) and ulv.…

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Q: B = = v= -6 3 6 109 1 -37 -20 -2 -2 -2 1 2 is an orthogonal basis of Rª. Find [v] Fo

A:

Q: n (c) Find a vector b in R³ such that the solution set of Ax = b is a line in R³ parallel to the…

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Q: linear algebra

A: To prove the linear independence of the three given vectors.

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.