3 4. Let u =-3 and A= 1 1 Is u belongs to the plane in R' spanned by the -6 -2 -8 columns of A? Why or why not?

Q: Find the cross product a × b. a = (9, 0, -4), b = (0, 8, 0) Verify that it is orthogonal to both a…

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Q: The dot product of two vectors can be written in the form x = 00 s+ X1 X2 and y = in R" is defined…

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Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: 3 = [2 +21 Verify Properties (vi) and (viii) in showing C²x2 is a 2+2i 4+i Let c₁= 21, C₂ = 1 + 2i,…

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Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

Q: 42. Rather than use the standard definitions of addition and scalar multiplication in R®, let these…

A: The given question can be solved as shown in step2.

Q: 2.b) Which vector is not normal at the plane defined by 2x - 4y-6z+1=0?

A: The solution is shown in step-2

Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

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Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

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Q: Write a scalar equation of each plane. a) [x, y, z] = [2, -5, 4] + s[2, -3, −2] + t[7, -3, 5] b) [x,…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: Let a, 1 1 -7 -7 3 and b = 3 15 h For what value(s) of h is b in the plane spanned by a, and a₂?

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Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

A: The scalar equation of a plane is of the form: ax+by+cz+d=0, where a, b, c ,d are constants. The…

Q: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a…

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Q: Let u = h = , V= -3 7 2 and w= For what value of h is w in the plane spanned by u and v?

A: The given vectors  and .The objective is to find the value of  for which  in the plane spanned by…

Q: Consider the vectors u₁ = and the vector w = 3 H Q- W U2 = []} Uz = U2+ →→→→ →→→→ If u IS in the…

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Q: 1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*. (a) Examine if vector X = (-4,-1,6,12) is in…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

A: Given u1+u2β=5,4t, and the change of coordinate matrix Q from β' to β is Q=1c3d. Express v1 as a…

Q: Find four vectors v1, v2, V3, v4 in R such that 1. no two are collinear (in particular, none of the…

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Q: A = x6- y9+z3 B = x6- y3+z9 C = x 2- yl-zl For the given vectors A,B, and C show that whether C is…

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Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

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Q: (-4,2+i, 1), and y = (i, 5, 1 + i) be vectors in C. Compute (r, y), Let z = ||x||, ||y||, and ||r+…

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