5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1), (2, -3)].

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: the vectors î+ cos - cos (ß- α) } + cos (y - α) k, cos (a − B) i + j + cos (y – B) k i + cos (B-y)…

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Q: Calculate the component of v = 〈− 2, 1/2 , 3〉along w =〈1, 2, 2〉.

A: Given: Vector, v=-2,12,3 Vector, w=1,2,2

Q: F(x, y, z) = (z sint z sin(ar), e²y-2 X b+y

A:

Q: Find the coordinate vector of p relative to the basis S = {P₁, P₂, P3 } for P₂. p = 15 - 20x + 6x²:…

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Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: vectors i + cos (P- j+ cos (y - a) k, cos and s (ß−y) ĵ+ak, where a, ß and y are different angles.…

A:

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: 5. Express u = (-4, 3, —2) using the unit vectors.

A:

Q: 9. Given that u = (1,5) and v = (-2,3), determine the following %3D -3u – 4v =

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Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

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Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

A:

Q: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

Q: Let l be a straight line that passes through the origin and is parallel to the vectors…

A:

Q: Compute the orthogonal projection of u onto v. Use the square root symbol '' where needed to give an…

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Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: 27. Determine the area of the parallelogram formed by the vectors u=[3,-2,5] and v=[-1,4,2].

A: Step 1:

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Let u = (2, -1,3), v = (3,0,1) and w = (-1,-1,3). find all values of I, m and n such that lu + mv +…

A: