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

Q: 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…

A:

Q: [2 1 0 - 1 1 1 1 Determine a basis for row(A), and null(AT). What are 0 2 -1 0 ons of each, and how…

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Q: Let S = {1+ 5x, 1 – 2x-}. Which of the following polynomials could be added to the set S to form a…

A:

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: 25. B = (f1, f2, f3) is a basis for R2[x] where fi = 1+ x + 2x², f2 = 1 + 2x + 5x², f3 = 2 + x +…

A:

Q: -6 Express the general solution of Ax =b where A = and 6 -12 -6 as x = x, + cx„ where x, is the row…

A: Given: Matrix A=3-66-12 and B=-6-12. The objective is to express the general solution of Ax=b.

Q: 1 3 S = 4 9. a basis for R3? Explain why or why not.

A:

Q: Find the degree and a basis for Q(√3 + √5) over Q(√15). Find the degree and a basis for Q(√2, ∛2,…

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Q: 1210 0 2 5 1 10 3 7 2 (14) Let A = 2. L4 9 3-1 4 -2 (a) rank(A) = %3D (b) null(A) = (c) Find a basis…

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Q: A 2-4 284-6 0 23 05 0 -5 6. 5. 2. 12 4-1 6. -9 15 L3 4 -58 a) find basis for col(A) Find basis for…

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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 vectors 6. 17 form a basis for R° if and only if k + 7

A:

Q: Suppose A E R4×3 has the following QR factorization A QR V2 -V2 [1 0 1 0 0 0 0 -1 1 1 1 -1 R = 1…

A: We will first find the matrix A using the QR factorization given.…

Q: The coordinates of p(x)=5+3x+x² relative to the basis {1+x,2-x2,3+x+x²} is O (-1,1,2) none (0,1,1) O…

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: 2 1. Find a basis for span(S), where S = -2 6.

A: Please see the explanation below

Q: -2 9 Consider the matrix A = Find a basis B -1 4 of R2 such that the B-matrix B of T (x) = Ax is 1 1…

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: Find all values of a for which {[a? 0 1]. [0 a 2].[1 0 1]} is a basis for R3.

A: let v1=a2 0 1 , v2=0 a 2 and v3=1 0 1 be the three vectors in R3. now these vectors forms a basis of…

Q: [ 4 -1 Find a basis for the null space of A = - 20 {le Ex: 1

A: If x belongs to null space of a matrix A then Ax is equal to zero.

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: 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: 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: 4 -3 v1 = V2 %3D form a basis for IR if and only if k

A: Solve the following

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…

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

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Q: (b) Calculate a basis C for S and state dim(S).

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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: S = (1 + x, 1 – 2x) is not a basis for P,(the space of polynomials of degree less than 2) Select…

A: False.

Q: 2. Consider the basis * B = (1+*+**, x +r, 2). %3D for P2. Let p(x) = -1 + x + 2r?. Then [p(x)]R =…

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: 2 1. Find a basis of the null space of the matrix B -2 -2 -4

A:

Q: See picture

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

Q: 4 2. If a basis for R3 is B = -3 and given [x]B find i in the standard basis.

A:

Q: Suppose A E R4×3 has the following QR factorization A = = QR V2 1 -1 1 |1 -1 V2 -V2 [1 1 0 1 -1 0 0…

A: Here, we need to find an orthonormal basis of A. First we will row reduce A to find the column basis…

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: 2. let A = 2 4 and W= d. Find a basis for NulA. e. Find a basis for RowA.

A: Given that, A=11102410-1 (a) The null space of A is of the form, X=x1x2x3 such that, AX=0. That is X…

Q: [3 9 5 : A=0 4 0 1 00 0 0J Find a basis for the null space of the matrix.

A:

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

A:

Q: Lemma 2.8 B is a basis of T iff

A: To prove that Β is a basis of Τ iff ∀Ο∈Τ ∃ Β0⊂Β: Ο=∪ ΒΟ

Q: 3. T: P, P, is defined by T(a, + a,x) = -a, + (a, + a,) B is the standard basis for P1, and B' =…

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Q: Find a basis for Q(3^(1/3), 3^(1/2)) over Q.

A: It is known that,

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…

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Q: (b) Find q if S is the basis in x2 + 1, x2 – 1, 2x – 1. (c) Find B if S is the basis in 3 -1 -12 1 В…

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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…

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Q: 12. Let B = {1+2x, x – x², x + x²}. (a) Show that B is a basis for P2. (b) Let p(x) =1+3x + x².…

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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⊥.

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.