Exercise 5.8.2 Let B = in R². Find CB(x). {[+][6][+])} 0 be a basis of R³ and let x = 5 -1 4 be a vector

Q: Let 6 2 A =| 9 5 11 8 L = 3 1 and 1 4 U = | 0 2 -1 Find scalars r, s, t, and p so that LU = A.

A:

Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

A:

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…

A:

Q: Find the 2 x 2 matrix P such that Pu is the orthogonal projection of in R² onto the line consisting…

A:

Q: 0. The vectors 2 0 , and 1 form a basis ofR. 3 3 a) True b) False

A:

Q: a) Any vector z ER" can be writ ten as a line ar combination of the stand ard basis vectors e1, e2;…

A:

Q: (0+0i) 0+0i 1+0i 0+ 0i 0+0i (1+0i is the standard basis for Cn as a vector space over C and again…

A: Basis: Let V be a finite dimensional vector space over a field F. A non-empty subset B of a vector…

Q: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

A:

Q: Find an orthonomal basis of U = span 2 00 -2

A:

Q: 127 (68) -100 -4 23 B = v= 27 is an orthogonal basis of R³. Find [v]⁄·

A: (.) Given orthogonal basis is,           and  vector (.) Orthogonal basis: A basis  is called an…

Q: Let S = {ax? + bx + a : a, b ɛ R}. Then a basis and the dimension of S are (a) basis: x2, x + 1;…

A:

Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

A:

Q: Consider the basis B of R² consisting of vectors Find # in R² whose coordinate vector relative to…

A:

Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

A:

Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

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

A: Applying nullity definition we have

Q: linear operator T: P,P2 4. Cet the be defined by T(aotq, Xfayxtagx?)=3ast (az-93)x² a) Find a basis…

A: The given linear operator is                                               T : P3→P2 which is…

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 coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

A:

Q: b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

A:

Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: Find the vector x determined by the given coordinate vector [x] B and the given basis B. 8) B =…

A:

Q: 1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are…

A:

Q: B = (f1, f2, f3) is a basis for R2[] where fi = 1+ 2x + a², f2 = 2+ 3r + 2x², f3 = 2 + x +3x². If…

A: The correct option is option (e) 1 + 2x²   The detailed solution is as follows below:

Q: Consider the basis B of R2 consisting of vectors [2] and [2] Find in R² whose coordinate vector…

A:

Q: Q2: Rewrite the following R4 vectors as an orthonormal basis: ------- = = 1 and (c) = 0 -1 2 1

A:

Q: Find the decomposition of a(t) into tangential and normal components at the point indicated. r(t) =…

A: Given a position vector rt=3-t , t+5 , t2 , t=2. To Find : Decomposition of atin terms of tangential…

Q: Consider the basis 8-{(!). (3)} 1 2 B = 2 of R2. What is the coordinate vector of (1) with respect…

A: Given basis is B=12,25 We have to find the coordinate vector of x¯=21 Let the coordinate vector of…

Q: Find an orthonormal basis of the plane x₁ + x₂ + x3 = 0

A: The given problem is to find the orthonormal basis of the given plane. Given plane is x1+x2+x3=0

Q: Find an orthonormal basis of the plane x12x2x3 = 0. 1 1 2 5 ਹੱਲ [廣告] Answer:

A:

Q: Let {1, 2, 3, 4, 5, 6} be the standard basis in R6. Find the length of the vector = 32₁ - 22 - 23 -…

A: Solution of the question is given below.

Q: The vectors B = [x] B= = {1+4) Show work in the exam 8 form a basis. Find a vector x given the…

A: Given that  B = 0-1 , 1-1 is a basis set.  The coordinate matrix of the vector X with respect to the…