[C] Is the system of vectors X1 = (2, 2, 1)", dependent? Ху — (1,3, 1)7, X3 = (1, 2, 2)" linearly

Q: The vector z = (2 + 2i) ( -V3 + i) lies in * the

A: The vector equation is z=2+2i-13+i.

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: Show that ex and e−x are linearly independent in C(−∞,∞).

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Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

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Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: For a C4 axis along z axis, please find the matrix for c, the synmetry opertion on a vector·

A: Given, C4 axis is along z axis . Upon action of C14 symmetry operation, the change with respect to x…

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3x−3y−4z=5 and…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: Consider the system X + 3x, + 2x3 7x4 8x, = 3x, + 4x5 = -5 -x 2.x, 2.x, 8x + + 8r, 8x5 %3D - (i)…

A: To find the solution of system of consistent

Q: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

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Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: If {v1, v2, . . . , vn} is a linearly dependent set of vectors, prove thatone of these vectors is a…

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Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

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Q: () - - (a + bt c+ dt) e *() -- () a (:) - (-) A d - c

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Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: what is the dimension of the vector space formed by the solution of the system of the following…

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Q: Find a basis for the set of vectors in ℝ3 in the plane × + 2y + z = 0. [Hint: Think of the equation…

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Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: what is the dimension of the vector space formed by the solution of the system of the following…

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Q: At what value of k are these vectors collinear?

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: what is the linear combination of  u⃗  and v⃗ ?

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Q: verify that the given vectors are solutions of the given system. Then use the Wronskian to show that…

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Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

Q: Verify that the vector X is a solution of the given homogeneous system. -1 X' = 4 X; x = -3t/2 1 (*)…

A: Given the homogeneous system is x'=-1141-1x x=-12e-3t2

Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: for any R value of the third, so that the following vectors are linearly related and loudspeaker…

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Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

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Q: The set of vectors u1 = , and u2 = are %3D having rank 3 Linearly independent having rank 1…

A: Given- The set of vectors u1=<1,-1,3,-1> and u2=<1,-1,4,2> To Check- If they are…

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

Q: Find the vector form for the geveral selution to the system of equations. X, - X, + Zxg - xy - Xx=-8…

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Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: +0, then the matrix H = I – 2- vv7 is orthogonal and symmetric. Show that if the vector v

A: Given  H=I-2vvTvTv

Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: on vectors for t2 0.

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Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

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Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: Suppose you solved a second-order equation by rewriting it as a system and found two scalar…

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