How do you know that for all a, b, c, d: ax + bx will be orthogonal to cx? + d ?

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: Use Cramer's rule to fins a solution: 3x-2y=4 6x-4y=0

A: Cramer’s rule:

Q: Express the following: as a linear combination of u = (2, 1, 4), v = (1, -1, 6) and w = (2, 2, 8).…

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Q: AB is orthogonal

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Q: D. Prove i [- 2,5, 1], 7 = [2,1, – 1] and w [- 6,0, – 12] are orthogonal. %3D

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Q: Let S in Mzx2; a + 2d=0 and b-2c 0 with the standard %3D operations in M2x2 Which of the following…

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Q: Find b and c so that  (9, b, c)  is orthogonal to both  (1, 2, 7)  and  (1, −2, 1).

A: To find b and c so that (9, b, c) is orthogonal to both (1, 2, 7) and (1, −2, 1).

Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: Verify that det A = det B + det C, where Uj + vj U2 + v2 Uz + V3 A = A22 аз1 A32 --EE-E: A12 A22 V2…

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Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: What is the difference in ndahin befween matnx multiplicatin and fensor multiplicahin of two lensors…

A: The tensor product V ⊗ W of two vector Spaces V and W (over the same field) is a vector space,…

Q: 5. What is UF, where F = Ø? Prove the correctness of your %3D | computation. answer

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Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

Q: Find a non zero unit vecor î that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: The given vectors are u1=(1,2,1) and u2=(2,5,4) in R3

Q: Solve using Cramer's rule. 2x+8y = 11 4x+6y = 3 %3D %3D

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Q: as the sum of two orthogonal orthogonal to ư

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Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: mple. Compute AB and BA where 1 -1 A = %3D B = -2 2 3 4

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Q: Find ||u||, ||v ||, and ||u + v||. -(-1. 금), v-(2.-3) v = (2 - ± ) u = 4 (a) ||u|| (b) ||v|| (c) ||u…

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Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: Verify that it is orthogonal to both a and b. (a × b) · a = (a × b) · b = %3D

A: Given

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: All Orthogonal all the time is always better True False

A: Given: Statement : All the Orthogonal all the times is always better

Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

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Q: Determine whether v = 3i - 5j and w = 6i - 10j are parallel,orthogonal, or neither.

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Q: Find mZB. 141° 72° B 47° mZB %3D Submit

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Q: 21. Apply the conjugate-gradient method to the problem Ax = b, where 1 A = 1 1 %3D and b = 1 Verify…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w? Explain your…

A: Given that 'x' is orthogonal to 'v' and 'w' . This implies x,v=0and x,w=0

Q: Find a non zero unit vecor û that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: Cross product of two vector is perpendicular to both vectors.

Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: |(u+ v) x (u – v)I = 2|u x v|

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Q: The vector (1,0, 0) is orthogonal to (0, 1, 1). O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

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Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

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Q: Find the condition for the two lines to be coplanar. a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2 az…

A: The given lines are    a1 +b1x+c1x+d1=0a2+b2x+c2x+d2=0a3+b3x+c3x+d3=0a4+b4x+c4x+d4=0  To examine…

Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: Answer each of the following as True or False justifying your If X and Y are linearly independent…

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Q: Find a non zero unit vecor ô that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: We have to find a non-zero vector V that is orthogonal to u1=1,2,1 and u2=2,5,4 in R3.

Q: Verify that the two expressions are equal using the followi vectors Á = az + 2a, + 3a,, B = ax – ay…

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Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

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.