3. Given [1 0 1 A = 3 2 5 lo 4 4 -4] Find a basis for the following. Col A Nul A 1 0 1 |-- - 10 1 1 0 0 0 (a) (b) (c) Row A

Q: D) How do you know that T: P3> P2? (How do you know that the codomain is correct?) E) Find T(x + 2x?…

A: Given, T(p(x))=p'(x)-xp"(x) (D) p(x)∈P3⇒p(x) is a polynomial at most of degree 3. ⇒p'(x) is a…

Q: You are given that 1 1 -1 3 3 can be -2 -1 row reduced to 1 0 -2 0 1 0 0 0 Given that p1 =1- x, P2 =…

A: Both the statement is false see below the explanation

Q: [1 Given A = 1 3 1 2 3 1 1 Find basis for orthogonal Complement for C'(A). 1 0 8

A: Given matrix is  A=113123111082 To find a basis for the orthogonal complement for CA It is known…

Q: -1 Express the general solution of Ax = b where A = 3 and 3 1 as x = x, + cx, where x, is the row…

A: It is given that, Ax=b where, A=-1-133 and, b=1-3

Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: In Rª, let S = {(1,2,2, –1), (0, –1,4, 2)} and T = U = sp(S) and W = sp(T). Find a basis for U +W…

A: Your approach is absolutely right!

Q: -2 -1 -2 -4 4 -6 -5 -4 -4 6 10 -13 - Answer / compute the following. 7 7 -7 -5 -6 -9 10 -4 -3 -4 -6…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 1 -2 0 3 27 2 -4 1 Problem 1. Let A = 1 %3D -2 1-1 3 3 -6 2 1 8 (a) Find a basis for R(A) consisting…

A: R(A)= Col(A)column space of A so R(A) will have the same basis as Col(A)

Q: 4. Determine if B = {1,2 – x,3 - x2, r + 2x2} is a basis for P.

A: Given

Q: Question 2.b. Show that if char(x) has distinct roots, then there exists a basis v1....vn with…

A: To prove that the linear operator L can be represented as a diagonal matrix , under the given…

Q: Complete the standard basis for R². Ex: 5 1

A: The basis of the vector space V in ℝn is the n number of linearly independent vectors which spans…

Q: Explain why S is not a basis for P2.S = {−1, 11x}

A:

Q: 4. Use the matrix A to answer the following questions. 11 51 4 A = -6 -7 -1 2 1] -2 3. -3 4 4 a.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 15 tig = 12 0. 6. form a basis for R if and only if k #

A:

Q: 7. If a basis for R3 is B = and given [x]B =0 , find ž in the standard basis. 4 Consider the basis C…

A:

Q: Let M = {(, ¿ )-G i )G : DC : D Then M is a basis for M2,3 the above M3,2 the above O None of the…

A: Given that     M=110000, 110010, 100101, 100001

Q: Question 31 Determine whether (V₁, V₂, V3} is a basis for R³. -3, V₂ = 8, V3 = 3 O Yes O No

A: Sol:- It will basis for R3 Only when , they will be linearly dependent i.e. determinant should be…

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: Given that p1=1−x, p2=5+3x−2x2 and p3=1+3x−x2, consider the following statements:   1.  {p1,p2,p3}…

A:

Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

A:

Q: 4. Use the matrix A to answer the following questions. utot s (eto A = 51oy evenariW ovis on ab 11 4…

A: Since you have asked multiple subpart, we will solve the first three…

Q: Let B = {1+x, 1 – x², x + 2x²} and p(x) = 7+ 10x + 11x². You are given that B is a basis for IP2.…

A: NOTE: Refresh your page if you can't see any equations. . write all polynomial as a vector

Q: Show that B = {1+ 2t, t – t2,t+t2} is a basis for P3. ) Let p(t) = 1+3t +t. Compute [p(t)]s- (a) (b)

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Problem 1. A. Prove that B = {1+x, x+x?,1+x²) is a basis for P2 second degree polynomial space

A: Basis: Let V be a vector space, then a set of vector B={V1,V2,...,Vn} is called basis of set V is…

Q: -2 1 4. Let v, = 4. 0 ,and v3 -4 Is {v1,V2.V3} a basis for R? V2 = %3D 0. %3D %3D -4 - 4 - 4 O No…

A:

Q: 7 Find w if (w)s = |0| relative to the basis S = 3 – 10 3 W =

A:

Q: 3 6. (c) Find B if S is the basis in 3 -12 -1 2 B = .... ......

A:

Q: -2 -1 -2 -4 4 -6 -5 -4 -4 Answer / compute the following. 7 7 -7 -5 -6 -9 6. Let M = 10 10 -13 10 -4…

A:

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: If {e², e-², e2=} is a basis of solutions of y" + ay" + by + cy = 0, then c= (A) -1 (В) -2 (C) 2 (D)…

A:

Q: (G ) m - (; :) m - (; ).m - (; ) 1 1 1 3 1 2 4 Let mi 1 1 2 4 3 5 , m4 = 3 C1 1 4 C2 M= (m1, m2, m3,…

A:

Q: 1 25 21 - 20 1 -1 3 – 4 A matrix A= 1 61 51 - 54 reduces to 4 4 - 4 3 91 76 - 75 3 -1 Find a basis…

A: see the calculation below

Q: 13 5 -1 -3 1 2. Let A = 0 2 3 b 1 5 2 15 8 a) Find an orthonormal basis ст сти LO 28

A: Follow the steps.

Q: 1 2 1 251 1 3 7 2 2 4 9 3 - Given A = 1 Find the basis for nullspace of A. HA 3 3. 1 a. b. С. d. 1…

A: A=121025113722493-1

Q: See picture

A: Does the set L of two vectors form a basis for the subspace S?

Q: -2 -11 TO 1 The coordinates [Aleof A= with respect to the basis B= 0 -1 ] 2 of M2x2 O a. -1 -2 O b.…

A:

Q: 1) Let W = la + 2b + 1c + 8d la + 3b + 2c + 10d 3a +10b+7c+32d 2a + 8b+ 6c + 24d -5a + (-13) b +…

A:

Q: Find a basis for (null(B))+, where 1 2 -1 -3 2 2 4 -2 1 4 B := 1 2 3 -1 -2 1 2 11 -11 -10

A:

Q: Question 5 Justification is not required. Answer the following questions. [1 0 3 A =1 4 1 10 3 a)…

A: b) A and B are two 3x3 matrices with det(A) =-2 and det (B)=-3.            To find  det (4…

Q: 1. Let {w₁, W2, W3} be an orthonormal basis for V. Given that v = between v and w₁ is 0 = 60° and…

A:

Q: -2 0 1] 2 1? 1 Which of the following is a basis for the column space of -1 -4 2 4 27 2 | 2 1 -1 2 2…

A:

Q: 1. Explain whether S = {1, 2x, x² – 4, 5x} is a basis for P2 or not.

A:

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: 7.1 7 (omsider the Limear frams fomation T: R^→R" whore mahix A velative to the stan dom d basic is…

A:

Q: 10 2 1 4 5. Let A= 1 130 4 10 20 3 • What is RREF(A)? o Find a basis for R(A). • Find a basis for…

A:

Q: Problem 11. Suppose {v1,..., Vn} is a basis for V. Find conditions on c1, ..., Cn so that {c1v1,..,…

A:

Q: S = (1+ x, 1- 2x) is not a basis for P,(th

A:

Q: Solve using the concept of rank.

A: We write the matrix representation of S to get the answer. Recall that B=1000,0100,0010,0001 is 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.