1A Given the vector space (R³(R),+,-), two bases of S ={e1,e2,e3}, ei=R³, i= {1,2,3}, S'={u₁,12,U3}, where, u₁=(-1,0,1), u2=(1,1,1), u3=(0,1,-1) and the linear transformation f: R³ R³: (x,y,z) →ƒ(x,y,z) = (3x+2y, -x, z). -1 -1 1 --639 1 4 -1 0 -2 is the transition matrix from basis S to basis S', then Compute the representation matrix [f]s,off with respect to the basis S of R³, such that the matrices [f]s and [f]s' are equal. If, P = 1

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

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Let ā= −i − 2j + 3k, b = i - 2j + 3k, c = −i +2j - 3k.

A: The given vectors .The objective is to find the vector that is perpendicular to both  and .

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)…

A:

Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

A:

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: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: = Complete the following truth table. Use T for true and F for false. You may add more columns, but…

A:

Q: 5. Consider a unit vector u = (a,b). (a) How many unit vectors are orthogonal to u? (b) Explain a…

A:

Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a unit vector with positive first coordinate that is orthogonal to the plane through the points…

A:

Q: Let a and b be vectors in R" such that ||a||=|| b||=2 and (a,b)= — . Then ||a - b||= ...

A:

Q: Four vectors: a = [0 2 2], b' = [1 0 -1], c' = [1 2 4 8], d' = [1 2]. Compute each of the following…

A:

Q: Find a set of vectors {ü, ī} in R' that spans the solution set of the equations w - 1 - 2z 1 5w + 2z…

A: The objective is to find the the set of vectors that spans the  solution set of the equation.

Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

A:

Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

A:

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

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: For the vectors x=(1, -1, i, -i) and y=(1, i, -1, i) find the span(x,y)

A:

Q: 11) For u = (2,3,-1) and v (-1,01) find; %3D II a) proj,(u) b) The vector component of u orthogonal…

A: For finding projection using the formula, projv(u)=v→.u→v→2v→ The vector component of u orthogonal…

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

A: