3. Let V = P (R) (or P(R) if 2 = 0). How many vectors does a system of linear inmependent vectors in V have? 4. Let U be the set of solutions of homogenous equation: + y + z+ 2t = 0

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: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

A:

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: Given that the system zy² + zu + v 2r+ 2y-uv 2 zu + yu – ryz = 1 at (u, v) = (1,1)? can be solved…

A: Given system of equations as follows, xy2+zu+v2=3x3z+2y-uv=2xu+yv-xyz=1

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: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

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: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

A:

Q: 16 Jlg wo vectors ñ and m are said to be orthogonal if ħxñ=0 ulgo O ihs o

A: Two non-zero vectors are said to be orthogonal when (if and only if) their dot product is zero.

Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

A:

Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

A:

Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

A:

Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…

Q: Given that the system xy² + zu + v² = 3 x³z + 2y – uv = 2 xu + yv – xyz =1 can be solved for x, y,…

A: Given that,

Q: 2. Rearrange the equations to form a strictly diagonally dominant system. Apply two steps of the…

A: The complete solutions are given below

Q: 14 Verify the given linear approximation at a = 0. Then deter-

A:

Q: Use the indicated entry as the pivot and perform the pivoting. $3 z 0 0 60 o ol 80 1 0 300 0 10 X1…

A:

Q: irst verify that the given vectors are solutions of the given system. Then use the Wronskian to show…

A:

Q: what is the dimension of the vector space formed by the solution of the system of the following…

A:

Q: Suppose vi, V2, V3, b, d are vectors in R". Further suppose that -vi + v2 + vz = -b, 2v1- 2v2 + v3 =…

A: Given v1,v2,v3,b,d are vectors in Rn.-v1+v2+v3=-b ,…

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: what is the dimension of the vector space formed by the solution of the system of the following…

A:

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

A:

Q: 21. Apply the conjugate-gradient method to the problem Ax = b, where 1 A = 1 1 %3D and b = 1 Verify…

A:

Q: Verify that the vector X is a solution of the given homogeneous system. -1 X' = 4 X; x = -3t/2 1 (*)…

A: Given the homogeneous system is x'=-1141-1x x=-12e-3t2

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

A:

Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=

A: Given that, u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v

Q: Suppose column 5 of U has no pivot. Then x5 is a __ variable. The zero vector (is) (is not) the only…

A:

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Find a set of vectors {u°, v*} in R4 that spans the solution set of the equations w-x-2y+3z=0…

A:

Q: If U and V are 2 x 1 orthonormal vectors and A = UVT then the trace of A is equal to а. О b. 2 с. -1…

A: We have to find Trace of the Matrix.

Q: Follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in…

A: We have to find the solution set of the homogeneous system…

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0,…

Q: (bj Prove that if in a system of non-zero vectors they are pairwise orthogonal, the system is…

A: Given: Consider the system of non zero vectors and they are pairwise orthogonal,  and show that…

Q: (1) Suppose that {r, y, z} is a linearly independent subset of vectors in R". Show that {x - z + y,…

A: Result:  A set of vectors v1, v2, …, vn is said to be linearly independent, if a1v1+a2v2+…+anvn=0…

Q: Given a vector y e Rd and a scalar A> 0, consider the following opti min 히lx-yll + 세제i. XER 2 Please…

A: Given, minx∈ℝ12x-y22+λx1. Let, f=12x-y22+λx at the optimal solution gradient of f is zero. ∇f=0 As…

Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

A:

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: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

Q: Suppose that the solution set of the homogeneous system Ax = 0 is given by the formulas x - - 5r +…

A:

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

A:

Q: For a given vector a E R" and scalar A > 0, show that the following problem 1 minx, ||x – all +A…

A: Given: A vector a∈ℝn and a scalar λ>0   To show: The problem minx12x-a22+λx2 has the optimal…

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: Suppose you solved a second-order equation by rewriting it as a system and found two scalar…

A:

Q: A. If the grades of the students in linear algebra and vector analysis is set to be x and y…

A: Let us denote X as the grade of linear algebra and Y as the grade of Vector Analysis. A. Excel…