Consider the basis B of R2 consisting of vectors [2] and [2] Find in R² whose coordinate vector relative to the basis B is [7] B 18 = = =

Q: Write the vector v = B - - -3 8 5 -44] 50 24 1 - as a coordinate vector with respect to the basis

A:

Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

A:

Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

A:

Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

A:

Q: W₁ = B W2 = (9) where a ER, BER. (a) Give an expression for ww2 (b) Does the linear independence of…

A:

Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: Find the vector projection of v = -6i + 10j – konto w = = 2i + j − k (Give your answer using…

A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

Q: Represent the vector with respect to each of the two bases { ] y = B = B2 =

A:

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: 2. In each question, explain the reason. Consider the following vectors in R³: (a) (b) v₁ = (1, 0,…

A:

Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

A:

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

Q: For the three given vectors, either show that they are linearly independent or find a nontrivial…

A:

Q: For the vectors A = ux + 3uy + 5uz, B = 2ux + 4uy + 6uz, and C = 3ux + 4uy + 5uz, show that A × ( B…

A: For the given vectors A,B,C show the given property  If A=a1ux +a2uy+a3uz and B= b1ux+b2uy+b3uz then…

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…