4 1 7 19. Let vi = -3 V2 = V3 = 11 and also let 7 -2 6. Span {v1, v2, V3}. It can be verified that 4v1 + 5v2 – = 0. Use this information to find a basis for H. There is 3v3 H more than one answer.

Q: The set B=(3+2x², 12+2x+8x²,- (29+6x+20x2)) is a basis for P2. Find the coordinates of p(x) = 8 + 4x…

A: Solution :-

Q: Le: S= {1-x+x²,1+ 2x, – 1+ 2x} and p= - 4 +8x – 4x². The se: Sis a basis for P2. (P)s = (a,b,c) with…

A:

Q: } 4. You are given that B = {1– 2x + x?, x+ x?, 2 +x – a?} is a basis for P2. (i) Find the…

A:

Q: (a) Find the basis for the solution space of I1 +a2 - a3 = 0, -2.r1 - 12 + 5rz = 0, -21 + 4r3 = 0…

A:

Q: 2) Let T(a+bx+cx² + dx³) = i) A basis for Ker(T) would be: ii) The Nullity of T is: iii) The Rank of…

A: As per our guidelines only first Question is solved. To get solution of remaining question kindly…

Q: Let V = P2(R). Show that 3 = {1+r+2²,x+r², x²} is a basis for V. [You may assume that we already…

A: We will use the fact that if DimV =3, then any subset of P2(R) consisting of three linearly…

Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: 32. Let p, (t) = 1 +t², p2(t) = t – 3t², p3(t) = 1 +t – 3t2. || - - a. Use coordinate vectors to…

A:

Q: The first three Hermite Polynomials are 1, 2t, and − 2 + 4t2. (a) Show that the first three Hermite…

A:

Q: 18 Given the basis B -2 1 7 7 if the coordinates of w relative to basis B are wB - 4 find w 2

A:

Q: -4 1 1 Find a basis for the orthogonal complement of the column space of A = -1 (That is, find a…

A: Given  A=-411-132-65 to find the basis for (col(A))⊥

Q: За + 6b — с ба — 26 — 2с - Find a basis for H = : а, b, с €R -9a + 56 + 3c | -3a + b+ c

A: Given H=3a+6b−c6a−2b−2c−9a+5b+3c−3a+b+c:a,b,c∈R We have to find the basis for H. First write the…

Q: -{)--- 00 1 1 Let vi = 1 2 and set 3 V2 = 1 4 V = {x € R* : x · vị = x · V2 = b1 = 0}. If a2 b2 is a…

A:

Q: GE)- 7. If a basis for R3 is B = and given [x]B = find i in the standard basis.

A:

Q: LetT :R4 →R3 be defined by T (a, b, c, d) = (a + 3b − 2c + 4d, b − c + 2d, −2a − 6b + 4c − 8d).…

A:

Q: (4) 10. Let H = {r+2x2, 1+ ka?, k + (2k + 3)r2} (a) For what value(s) of k is H linearly dependent?…

A: This belong to linear algebra.we check linear independence for the given vectors and find k so that…

Q: 6.4 H 6 Suppose A is Hhe matia for T: R²→R relative to the standand basis. Find the velative to the…

A: Consider the matrix A and basis B’.

Q: 9) a) Find the standard coordinate basis for the and B1 = = B -1 b) What is the coordinate basis of…

A: (b) Given :- The coordinate basis of xy in the basis B2 = -1420

Q: Find a basis for the subspace 96 4a + 6b W = E R2x2 a, b eR} of R2x2- 86 5a Ex: 1 4 6. A basis for W…

A:

Q: a) Find the basis for the solution space of I1 +a2 - r3 = 0, -2r1 - 12 + 5r3 = 0, -11 + 4r3 = 0 %3D…

A: (a) given system of linear equation x1+x2-x3=0-2x1-x2+5x3=0-x1+4x3=0 to find - basis for solution…

Q: The set B = {3x² – 4, 152² – (20 + 2x), 38 + 4x – 27x²} is a basis for P. Find the coordinates of…

A: Given, the set B=3x2-4,15x2-20+2x,38+4x-27x2 is a basis for P2. We have to find the coordinates…

Q: 17 37 Consider the orthogonal basis B = -3 10 of R³. -3 1 -9 11] Let V = -16 7 а If vB= |b|, what is…

A:

Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: Suppose S= {Pi;P2•P3;P4,P5;P6} is a basis for P5 and p is a polynomial of degree 4. Then the…

A: Given The coordinate vector is a vector in which each component is the coefficient of the linear…

Q: Given the ordered basis B = {p1 =1– 1, P2 = 4 – 7x find [p]B, the coordinates of p = -7+ 10x with…

A: Follow next step

Q: 4. Find a basis of each vector space below and hence write down the dimension of the space. You do…

A:

Q: 1 4 Let v = | -9 | v2 = V3 = -8 and H = Span (v,,V2,V3}It can be verified that 4v, +2v, – 3v, = 0.…

A: As it is given that 4v1+2v2−3v3=0   ...(i) implies  v1,v2,v3 are linearly dependent from (i), we get…

Q: . ) The set B = {4x² – 4, 4x – 20 + 20z², 37 – 8z - 36x²} is a basis for P. Find the coordinates of…

A:

Q: Let V = span {1+ 2x – x² + 3r³, -2+x+x² – x*, -1+ 8r – x² + 7r", 3 + x – 2r² + r'}. Find a basis ß…

A: Step:-1 Note:- To span V we need the polynomials of degree 3, so dimension of V is 4. (think using…

Q: Q#3: Let V= P(R), and for P) EV, defme f,f EV by f(PW)= PE)dt and (Po)= Pe) dt. Find a basis for V…

A: Consider V=P1(R)  defined by                                 f1(p(x))=∫01p(t)dt      and…

Q: R4 Span {v1,..., V4}. Explain why {v1,..., V4} Is a basis for 4

A:

Q: 4 8 Find a basis for the column space of A = 1 2 {[ ]} 4 Ex: 5

A:

Q: The set B = {1– 2t + t2,3 – 5t + 4t² , 2t + 3t²} is a basis of P2. Suppose C = {c1, C2, C3} is…

A:

Q: B = {3 – 3x, 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x…

A: We have to find the coordinate vector of P(x)=4+2x-6x2. w.r.t the basis…

Q: T1. Find a basis for the column space of 2. 6. 8 4 12 3 9. -2 8 6. 18 6 A = | 3 9. -7 -2 -3 -1 2 6 5…

A:

Q: = {W₁, W2, W3} is a basis for R³, where 1 3 H W2 = 3 W3 -2 -4 Determine if the set B W₁ = 2 9 = -3 A

A:

Q: 1 .! Determine if the vectors 0 and 1 span R³. -2 3 Can these three vectors form a basis for R.

A:

Q: Let V = span {V1, V2}, where V1 and V2 = 1 2 Find a basis S for R3 that includes vi and v2.

A: Let V  = span { v1 , v2}  where   v1= 102 and v2 = 111 Find a basis S for R3 that includes v1 and…

Q: Find [ℚ(sqrt2, i ) : ℚ] and a basis for ℚ(sqrt2, i ) over ℚ.   [Hints: Use the degree and a basis…

A: Find ℚ2,  i: ℚ and a basis for ℚ2,  i: ℚ over ℚ.

Q: 10. The solution set to the equation Ax = b is 1+t1 2 - t t + u :t, ueR} when b %3D L2t· - u a) How…

A:

Q: Which of the following is a basis for P3 (R) when viewed as a vector space over R with the usual…

A: Given are several vector spaces. We need to select those vector spaces that forms a basis for ℘3ℝ.

Q: 1 3 Let A = -1 -2. Find a basis for Col(A)+. -3 16 A basis is {v1} where V1 =

A: Given is a matrix A. To find: Basis for perp of Col(A)   First we find Col(A) from the given matrix…

Q: s = (6 4 1) (3 −5 1) (8 13 6) (0 6 9) explain why S is not a basis for R3

A: Given S=6,4,1,3,−5,1,8,13,6,0,6,9. We have to explain why S is not basis of R3. Definition:- The…

Q: T1. Find a basis for the column space of 2. 6 8 12 3 9. -2 8 6. 18 6 A = | 3 9. -7 -2 -3 -1 2 6 18 4…

A:

Q: [7 2 4 6 What is [A]B, the coordinates of A = with respect to the standard 10 0 1 basis B = of R2x2?…

A:

Q: 1. Use coordinate vectors to show that (4-t), (3-1), 2-t,and 1+5t-6r +f form a basis for P. Then…

A: To check that the polynomials 4-t3, 3-t2, 2-t, 1+5t-6t2+t3 form a basis for P3. We will write the…

Q: a b 1) Let T cla + 2b + 1c + 3d + (-11) e+ (-la+ (-1) b + (-2) c + Od + 7e) x. d to Then a basis for…

A: The given transformation is  Tabcde=1a+2b+1c+3d+-11e+-1a+-1b+-2c+0d+7ex To find a basis for KerT⊥.

Q: 1 3 0 1 1 1 1 and v3 2 3 4. Let A = V2 16 -3 1 3 1 -1 -1 You are given that {v1, v2, v3} is an…

A:

Q: Use the above to answer the following questions. 7.1 Find a basis for the nullspace of A. 7.2 Find a…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.