7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3, X = (X₁, X₂, X3),Y = (₁,2,3) and the vectors u₁=(1,-2,1), u2=(-1,2,0), u3=(1,-1,1), u4=(0,1,1). Find the linear mapping ƒ:R³ →R³, such that ƒ (u₁)=(4,0,4), ƒ(u₂)=(-3,2,-3), f(u3)=(3,1,3), fƒ(u4)=(0,3,0).

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

A:

Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

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: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

A:

Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

A:

Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

A:

Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

A:

Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

A:

Q: Find a set of vectors {u, } in R4 that spans the solution set of the equations {2w- w-x+z = 0, 2w +…

A:

Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors <1,1,0> and <0,1,1> to get a cross product for a…

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

A:

Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

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

Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

A:

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: Use the function to find the image of v and the preimage of w. T(V, V2, V3) = (4v, - V, 4v, + 5v2),…

A:

Q: Find two different combinations of the three vectors u = (1,3) and v = (2,7) and w = (1,5) that…

A:

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

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: and .We have to find .

Q: What is the value of each of the constants that are part of the linear combination between the…

A:

Q: 7) Find all vectors v in F such that 2v + ) -)

A:

Q: 6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2…

A: