Question (a)
.
write all 3 vectors in the matrix
vector v is
system Ax=v is
solution is
so here coordinate vector is
.
.
.
.
Question (b)
.
write all 3 vectors in the matrix.
vector v is
system Ax=v is
solution is
so here coordinate vector is
.
.
.
Question (c)
.
write all 3 vectors in the matrix.
vector v is
system Ax=v is
augmented matrix is
the solution is
so here coordinate vector is
42 - 2x + 3 a coordinate vector with respect to the following 4. Write the...
6. (a) Let V be a vector space over the scalars F, and let B = (01.62, ..., On) CV be a basis of V. For v € V, state the definition of the coordinate vector [v]s of v with respect to the basis B. [2 marks] (b) Let V = R$[x] = {ao + a11 + a222 + a3r | 20, 41, 42, 43 € R} the vector space of real polynomials of degree at most three. Write down...
With explanation! 3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...
(1 point) Consider the ordered bases B-(_ (5 + 9z) ,-(1 + 2) and C-(1-42, 3} for the vector space P2 c. Find the transition matrix from & to B -2 2 -10 f. Find the coordinates of q(z) in the ordered basis B if the coordinate vector of q(z) in C is [q(z)]c g(z)] B
Let S = {t2.t-1,1} be an ordered basis for P2(t). If the vector v in P2(6) has the coordinate vector 2 3 with respect to S, then what is the vector v? Select one: O at2 + 2t +1 O b. +2 +1+1 O c. 12 + 2t - 1 O d. t2 + 2t
please show all steps Find the new coordinate vector for the vector x after performing the specified change of basis. 8) Consider two bases B = 61, 62, 63 and C = C1, C2, C3) for a vector space V such that b1 = C1 + 2c3, b2 = C1 + 4c2 - C3, and b3 = 301 - C2. Suppose x = 51 +6b2 + b3. That is, 8) suppose [x]8 = 6 . Find [x]c A) B)
please help. system is sensitive to answers. Find the coordinate vector (x]a of the vector x relative to the given basis B. 16 and B = (b, b2} b = b2 -4 -2 -5 28 O A. -64 -196 ов. -32 -64 32 D. 41 5. Find the vector x determined by the given coordinate vector [x]g and the given basis B. -2 -3 -3 -3 -5 -3 - 11 ОВ. хв - 20 18 OA X= 33 - 15...
Problem #11 : Let p-7x2 + 5x + 4 Find the coordinate vector of p relative to the following basis for P2, pi 1,P2 = 1+x, p3 = 1 +x+x2. =
Linear algebra: tell me what happen. How do we get that matrix A by using the D derivative D(x^2)=2x how we get D(x^2)=2x+0*1???? follow the comment EXAMPLE 5 The linear transformation D defined by D(p-p' maps P3 into P2. Given the ordered bases [r.x, and [x, for Ps and P2, respectively, we wish to determine a matrix representation for D. To do this, we apply D to each of the basis elements of P3 Convert t Microso Documen D(x) =...
Find the coordinate vector [x]g of x relative to the given basis B = {51,b2,b3}: 1 2 2 by = -3 b3 = b -1 x= -5 4 5 4 [x] = (Simplify your answers.)
Math 407 Homework 4 Name: 1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. b) v = {(7: «y 20} with the regular vector addition and scalar multiplication. with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t+t?} is a basis for P, the set of all polynomials with degree less than or equal to 2. Find the coordinate vector of p(t)-5+21+342 3. Let H =Span{ői, üz.us)...