4. Let = (x1, 22, T3) and ỹ = (y1, Y2, Y3) be vectors in R. Consider the function on R given by %3D %3D (7, ) = x1y1 - 2x2Y2 + x3Y3 Show that (, j) is not an inner product on R. Let i = (1, 2, 1), what is (7, 7)? %3D

Q: Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4,…

A:

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

A:

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: The dot product of two vectors Y1 Y2 and j = Yn in R" is defined by a · j = x11 + x2y2 + ...+ x„Yn-…

A: According to the given information, it is required to determine a vector in R3 that is perpendicular…

Q: .

A:

Q: Please solve this linear algebra question. Thank you

A: According to the given information, It is required to show that u, v, w are linearly independent…

Q: Consider two bases B= (b, b2) and C= (c, c2) for a vector space V such that b, =e, - 6cz and by =…

A: Given two bases  and  for a vector space V such that and . Also, given that and we have to find .…

Q: (a) a = (2, 6, 0) , b = (4, –1, 1) (b) a =i-j-k, b = }i+j- 4k

A: a) given that  a=<2,6,0> , b=<4,-1,1> a→=2i+6j+0kb→=4i-j+ka→×b→=ijk2604-11…

Q: In éàch párt, đétérmine whether the set of vectors is orthogonal and whether it is orthonormal w…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

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: Prove that if {y1,...,yn} is an orthogonal set of nonzero vectors, then the vectors {x1,...,xn}…

A: Let consider the orthonormal set of nonzero vector be {w1, w2 …wn} instead of {y1...,yn} and the…

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

A:

Q: Consider the set of vectors S = {2 – x + 4x², 3 + 6x + 2x², 2 + 10x – 4x²} in P2. Show that the set…

A: use linear independent vector definition

Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

A:

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

A:

Q: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

A:

Q: The dot product of two vectors Xị yi X2 and y y2 Xn Yn in R" is defined by x · ỷ = x1yi + x2y2 + ...…

A:

Q: Let f : R² → R be defined by S if (x, y) ± (0,0), 1³y? f(x,y) = if (x, y) = (0,0). Determine the…

A: According to the given information, it is required to determine a non-zero vector u = (h,k) for…

Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

Q: Which of the following describes a plane perpendicular to the vector n = (2, 1, -4) and contains the…

A:

Q: Consider the vectors z1(t) = and za(t) = .Which of the following statements is true about W(z,(t),…

A: We use wronskian formula to calculate the following that means we calculate it determinant of…

Q: Find an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

Q: Let ƒ : R² → R be defined by A if (x, y) # (0,0), f(r, y) = if (r, y) = (0,0). Determine the nonzero…

A: According to the given information, it is required to determine a non-zero vector u = (h,k) for…

Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

A:

Q: Find the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b:…

A: Given data:     The first vector is: a=<a1, a2, a3>=<6, 0,-2> The second vector is:…

Q: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

A:

Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

A:

Q: Find vectors x and y in R2 that are orthonormal with respect to the inner product (u, v) = 3u₁v₁ +…

A: The given problem is related with inner product. We have to find the vectors x and y in ℝ2 that are…

Q: 3. Use the Wronskian to determine whether the functions fi = e*,f2 sinx and f3 = x are linearly…

A: To find- Use the Wronskain to determine the functions f1 = ex, f2 = sinx and f3 = x3 are linearly…

Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: Let x and y are orthonormal vectors in R". Then ||x – yl| is a) o b) c) V2 d) 2

A:

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

A:

Q: 10) Find the cross product a x b and verify that it is orthogonal to both a and b. a =  j + 7k,…

A: Let's find.

Q: 6. Let y = 9 , U1 , U2 1 |3| L10] 1 Compute the orthogonal projection of y onto W = Span{u1, u2}.…

A:

Q: Let B = {v2, v2, . . . , Vk} be a set of orthonormal vectors, this is, vi vj 0 if i # j and v; · Vi…

A:

Q: If u = x²+2x-y and v = - 2xy - 2y, then the vorticity vector is - 3yk 10 -yk 1O IIO yk IIO

A: Given u=x2+2x-yand v=-2xy-2y

Q: In R3 with the inner product given by (z, y) = 411y1 + 3r142 + 3r2y1 + 6z2y2 + 4r3y3, let F be the…

A:

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

A:

Q: Let H be the set of all points in the second quadrant in the plane V=R^2. That is, H={(x,y) | x ≤ 0,…

A: Here in the question H be the set of all points in the second quadrant in the plane V=R2. That is,…

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

A:

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

A:

Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

A:

Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

A:

Q: Show that (x, y) = 4x1y1-7x2Y2 for vectors x = (x1, x2) and y = (V1 Y2) in R2 defines an inner…

A:

Q: Let ü = (u1, u2) be a unit vector in R2 and let f: R2R be defined by if (r, y) # (0,0), f(r, y) =…

A: given  fx,y=x2yx2+y2if x,y≠0,00if x,y=0,0 (a) find Du→f0,0 (b) find ∇f0,0

Q: Suppose that two vectors T and ỹ in R" are orthogonal, meaning their inner product satisfies ·g = 0.…

A: This is a problem of vector calculus.