3 Find the coordinate vector of x = -2 with respect to the basis -2 В 1 for R³. 6. incorrect orrect dont Ų lWhy. URlerstand -20 -116 3.

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

Q: Find the stable vector of 1 1 1 P = 2 1 3 3

A:

Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

A:

Q: [0 3 4 2]* v1 = [1 1 2 1]" %3D

A:

Q: Construct the vector 0.8 b+1.4 a having initial point P.

A:

Q: Construct the vector 1.1 b+1.5 a having initial point P.

A: Given,

Q: 46 4 and j -3 Express the vector v as a linear combination of a -12 y. ||

A:

Q: (i, 2, 3i), v = Co over C. Are these vectors linearly independent? Can they form a basis 5.…

A:

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

A:

Q: 5. (S.15). Let ит —D (-1,1,3), из — (2, 1, —3), из Find expansion of the vector v= (-3, 2, 4) via…

A: By using simple linear algebra we find expansion of v via vector u1 , u2 , u3

Q: i. Start with finding Two vectors u and v of R' which are linearly independent (you can see this by…

A: In the given question we have to find the the Linearly independent vectors in ℝ3. Concept: In a set…

Q: Assume that 0 < a <1 and 0 < b <1.Find the stable vector of 1- a a P = b 1-b w = [ ]

A:

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: Q2) A- Use two methods to create the vector x having 100 regularly spaced values starting at 5 and…

A:

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: Find the coordinate vector of v relative to the basis S = {v1,v2, V3} for R3. v = (-11,–17, 7) (3,0,…

A:

Q: Suppose T(v1) = w1 + w2 + W3 and T(v2) = w2 + w3 and T(v3) = W3. Find the matrix A for Tusing these…

A:

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Find the coordinate vector of w relative to the basis S = (u1, u2) for R?. Let ui = (5, –3), u2 =…

A:

Q: Write x as the sum of two vectors, one in Span fu1,u2,u3 and one in Span fu4. Assume that fu1,...4is…

A: Let x = v + wWhere v = a1u1 + a2u2 + a3u4        and w = a4u4.

Q: to = [0 3 4 2]" v = [1 1 2 1]"

A: Handwriting solution.  { v0, v1, e1, e4} forms a basis for R4.

Q: Find the stable vector of 7 P = 2/7 M5 iii

A:

Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

A:

Q: 3 Find the coordinates of y 7 relative to the orthogonal basis Uj = U2 = U3 = -2 -4 10 2 2 4 252

A: The solution is given as

Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

A:

Q: (g) Can a basis for R' contain 9 vectors? Explain why or why not. 1 (h) Normalize the vector v = 1 1

A: Result: If dimension of a vector space V is n then the every basis of V contains exactly n elements.…

Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

A:

Q: Find the coordinate vector of w relative to the basis S= = (u1, u2) for R. Let u = (2, –3), u2 = (3,…

A: Given

Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

A:

Q: Find the coordinate vector of v relative to the basis S = {v1, v2, V3} for R3. v = (-11,–17,7) V1 =…

A:

Q: (9) Find a vector parameterizat1on of the line r(t) which passes through the points P = (2, –6, 4)…

A: The given points are P=(2,-6,4) and Q=(3,5,-3). We have to do vector parametrization. We subtract…

Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

A:

Q: 3. 2 Find a non-zero vector in R* which is orthogonal to 1 and 2 1

A: Given vectors are 1234, 3121 and 2311. We have to find the non-zero vector in R4 which is orthogonal…

Q: 3. (a) Find the terminal point of the vector that is equivalent to u = (2, 3) and whose initial…

A:

Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

A:

Q: Construct the vector 1.4 b+1.7 a having initial point P.

A:

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

A:

Q: Find the stable vector of 1 2 4

A: The stable vector is the probability row vector w such that w*P=w Let , w= [ x  y  z ] So it becomes…

Q: a) Detemine whether this set of vectors is orthogonal? Q. No. 3 -2 8. 4 1 b) Detemine if the…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 8) Let A be an nxn ma tiX. vector b the equation Ax = b has more than one solution. Explain why A is…

A: Invertible matrices

Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

A:

Q: 4. Determine whether the vector functions are linearly independent. Show your work. 1 4². 2t 8t 2

A:

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

A:

Q: saly dla Determine whether the vectors v1=[12 1]^T, v2=[10 2]^T and v3=[5 6 7]^T are Linear…

A: Given vectors: v1=[1 2 1]T=121 v2=[1 0 2]T=102 v3=[5 6 7]T=567