Let wi = w2 = and set B = (w1,w2). Then B is a basis of R². (C 9). If T : R? → R² has matrix with respect to B and the matrix of T with a11 is a21 a12 respect to S = | then a1 +a21 + a12+a22 is equal to a22 a) -2 b) -1 c) 0 d) 1 e) 2.

Q: 6. Let V = R? and let S be the set of vectors {[:] S = {v1,V2, V3} -3 Is S is linearly independent?…

A: We have V=ℝ2,  S={v1, v2, v3}={12, -32-3, 1-1} We will first check if the set is linearly…

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

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Q: 4. Be T: R3 → RS , Linear copy is represented in the standard bases by the matrix: 1 -1 2 1 2 -2 -3…

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Q: 26. B = (f1, f2, f3) is a basis for R2[x]. If the change of basis matrix 1 3 from B to Sr, læ] is 1…

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Q: 00 O 0 b 4. If (x,y)=2u+4v, then a. (uv) does not span R². b. {u,v} spans R². c. {uv) is a basis for…

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Q: 2.) Determine whether S = {G.1).(1.0).(2,12,6)} is a basis for R. If it is write u = (6,3,6) as a…

A: Determine whether S=23, 52, 1, 1, 32, 0, 2, 12, 6 is a basis for ℝ3. A set of linearly independent…

Q: Which of the following vectors form an orthogonal basis? 2 [0] T- 1] 3 го а) -1 4 b) -2 3 剛 2 -2' 3…

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Q: Find the new coordinate vector for the vector x after performing the specified change of basis. 6)…

A: We are given that      x = b1 + 3b2  It is also given that        b1 = c1 - 5c2       b2 = 2c1 + 6c2…

Q: QUE d. 1x) 3.1. the change of basis matrix from B to C. 3.2. [x]c for x = 3b₁ + 4b₂ + b3. Let B =…

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Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: 2. The vectors v₁ = and V3 = 1 [] 2 [] 2 are a basis for the space R³. It is given that: 0 Q+A + C2…

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Q: 2

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Q: The set B = {1+t², t + t², 1 + 2t + t²} is a basis for P₂. Find the coordinate vector of p(t) = 1 +…

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Q: 1. Determine S = { -1}is basis for R°. If it is write the vector z = as a+ a linear combinations of…

A: We have S=abc,b+1c+1a+1,c-1a-1b-1 To determine the set is a basis of R3 or not.   The basis for a…

Q: 1 3 -1 - 7 Let P = -3 -5 v = 2 V2 and v3 = 3 . Complete parts (a) and (b). 4 1 5 a. Find a basis…

A: Consider the provided question, According to you we need to solve only part (b).   Given…

Q: Find the vector x determined by the given coordinate vector [x]B and the given basis B. -3 21) B =…

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Q: Let U = p E 4 (R): 1 -1 p = 0}. Find a basis of U.

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Q: Let TilP > Pz, the basis of NIT) T (ax²+bx+c) = 2Qx+ b. Then %3D is

A: Applying nullity definition we have

Q: Let B, D be the following two bases of R°: 2 -1 B = 2 4 D = -3 -3 a) Find the change of coordinates…

A: Given: B=222, -122, -320 and D=4-3-1, 0-3-4, 1-2-2  To find: Change of coordinate matrix PD←B from…

Q: . Consider the set of vectors in R³: It follows that (A) S is a basis for R³ (B) S is linearly…

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Q: 2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with…

A: Using gauss Jordan elimination method to find the value.

Q: Assume that: U1= -1 -1 u2= 1 And W=span {U1, U2}. -Find a basis to W-.

A: Here   u1 , u2 are two vector. W= span {u1, u2 } So, {u1 , u2 } is a basis . Now we found a basis ,…

Q: Find the dimension and a basis of U = r2s+t 0 -3r s-t r, s, tER

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Q: 5. Explain why three linearly independent vectors u,v,w in R³ form a basis for R³. (Hint: Consider…

A: Basis of a vector space :                               A non empty sub set S be a basis of a…

Q: B = (v1, v2, V3) and B' = (w1, w2, w3) are bases of the vector space V. The change of basis matrix…

A: Given vector u is in the linear combination of the vectors of the basis U So to transfer in the…

Q: Let W be the set of all vectors with z and y real. Find a basis of W

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Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1) form…

A: 5) Given  that  Let, So we have  .Hence Noted that .Because  Hence basis for subspace V of  is

Q: Determine whether or not the set of vectors S-(. l where -(1,1.1), - (1,2.3).-(2,-1,1) form a basis…

A: The subset S is basis of vector space Rn over field R if  S spans Rn and  S is linearly independent…

Q: 1) Write v as a linear combination of the orthogonal basis V₁,...,V using dot products: V= |; V₁ =…

A: The given vectors are v=23, v1=45, v2=-54

Q: Let W = span{(1,1,-1), (2,3,1), (5,6, -2)}. i Find a basis for W. ii. Determine whether the vector X…

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Q: In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³…

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Q: b. where 17. Consider a matrix A of the form A -a a? + b? v and w such that Av entries of v and w in…

A: A=abb-a,   a2+b2=1Let V→=xyA V→=V→⇒abb-axy=xy⇒a-1bb-a-1xy=00This is a system homogeneous linear…