Find the solution using LU Decomposition: w + 2x − y + z = 6 −w + x + 2y − z = 3 2w − x + 2y + 2z = 14 w + x − y + 2z = 8

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Find the cross product a x b. a = 5j 6k, b = −i + 2j + k Verify that it is orthogonal to both a and…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are

Q: Find the LU decomposition of the following system of equation and then find the solution (x1, X2,…

A: Given system of equations can be written as Ax=b where x=x1x2x3 ; b=25-3and A43-5-2-45880.We have to…

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

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Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: Find the cross product i x v where i = 2i +2j -3k and i = (- 8, – 6, 3). i x ở =

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Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: determine the solution set of the linear system: x3-x4=-2 x1-x2+2x4=1 -3x1+3x2+2x3-8x4=-7 write your…

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Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: If u = 2x – 3, thenx V2x – 3dx :

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Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: Find the value of β for which w =〈−2, β〉 is parallel to v =〈4, −3〉.

A: Two vectors are parallel if the angle between them is 0 or π. That is, the vectors are pointing in…

Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

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Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Find curl (2z i + 3x j+ 2y k). curl (2z i + 3x j+ 2y k) = )i + ( i )j + ( i i )k

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Q: If u = -i + 4j - 7k and v = 5i - 2j - 9k calculate the product of u . v  u . v =

A: Use the dot product for finding the product of vector .

Q: Find V. (F × G), if F(x, y, z) = 5xi +j+ 7yk and G(x, y, z) = xi+yj – zk. - V. (F × G) =

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Q: 1 [-1] 2 Let 2 , v2 0 ,V3 = where S = {v,,v,,v,}. %3D 3 Is V4 linear combination of V1, V2, V3?…

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Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (-2,3,2)

A: Find the equation of the plane perpendicular to the x-axis and passing through the point (-2,3,2)

Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: Divide the quaternion on the right 5 + 4i− 6j  of the quaternion 3i+j-2k

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Q: Soly

A: Given  u = ( -1 , 0, 1, 1)   v = ( 2, 3, -1, 0)

Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

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Q: Assume that (U)=110, n(B′)=55, n(A∩B′)=25, and n(A∩B)=27. Find n(A∪B)

A: For any two events A and B, it is known that n(A or B) = n(A)  + n(B) – n(A ∩ B).