Explain why S is not a basis for M22

Q: Find a basis for the null space of A

A: Consider the given matrix, A=-1-22-124-42 Convert the matrix into Row Reduced Echelon Form. Apply…

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

A:

Q: Explain why S is not a basis for M2,2.

A: Let's check if S is linearly independent or not. S will not be linearly independent if for some…

Q: Find a basis for the nullspace of A. 6. 1 - 1 A=5 - 4 -4 7 -6 (a) 3 2

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Q: Is the set S = {(0, 0, 6), (1, 5, 3), (0, 1, 2)} a BASIS for R? %3D a. yes C. either b.no d.…

A: If V is a vector space over F and v1, v2,... vn then these n vectors are said to be linearly…

Q: (6) Explain why the basis of Ker(T) answers the question.

A:

Q: Every basis for R4 contains

A: Every basis of ℝ4 contains ______________

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

A: Given

Q: Find a basis for the null space of A -3 6 -1 1 -7 A = 1 -2 2 -1 2 -4 5 8 -4 3.

A: Given    A=-36-11-71-223-12-458-4We first find reduced row echelon form of  A.      Applying…

Q: Write standard Basis of P4(x)?

A: P4(x) is a collection of polynomial degree atmost 4

Q: Find a basis for the null space of A -3 -1 1 -7 A = 1 -2 2 3 -1 -4 5 8. -4

A:

Q: Find a basis for the span of {[1, 3]", [-1, 3]T, [1, 4]T , [2, 1]T}

A: We have to find a basis for the span of   [1, 3]T, [-1, 3]T, [1, 4]T, [2, 1]T .

Q: How do you extened an independent set to a basis?

A: Thanks for the question :)And your upvote will be really appreciable ;) To understand this problem,…

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

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Q: Explain why S is not a basis for R3.S = {(7, 0, 3), (8, −4, 1)}

A: Basis definition:

Q: Determine if - w = {-2 5 |} -2 4 is a basis for R³. Justify your answer.

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Q: Let B= { }].[),A} be basis for IR Is B orthonormal ? O False O True

A: Applying orthonormal property we have

Q: Is the set S = ((0, 0, 6), (1, 5, 3), (0, 1, 2)} a BASIS for R? c, either a. yes b.no d.…

A:

Q: Suppose that in solving an LP, we obtain the tableau in Table 22. Although x1 can enter the basis,…

A: We know that, if in an LPP if all the elements of any column are less than or equal to zero then the…

Q: Which of the sets form a basis for R?? Explain your reasoning (if yes, why; if not, why).

A:

Q: Explain why S is not a basis for R2.S = {(4, −3), (8, −6)}

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Q: Write standard Basis of P4(x)?

A: Given vector space is P4x

Q: Is the set {(1,0, -1,3), (1,0, 2,0), (2, 1,0, 3), (0, 1, 2, 3)} a basis for R? Justify your answer.

A: We have to show set is a basis for R4  .

Q: 9. Let S = { (1,2), (4, 5), (0, 2)}. Check whether S is a basis for ?2?

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Q: Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

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Q: Let A = {(4,1,0); (1,0,-2); (0,1,-5)}. Then A is a basis for

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Q: Determine whether S = {1– x, 2x - 3x2,x2 - 2x3,2 + x3} is a basis for P3

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Q: Is S= { 2 3 2 3 1 1 a basis for M2.2 1 0 4 0 1 1 0 1

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Q: Find a basis for the null space and row space of A.   A=[1,5,7  −1,−4,−6  3,−3,3]

A: Given matrix 157-1-4-63-33

Q: Determine whether S is a basis for M2,2- 4 0 2 2 3 0 2 0 O sis a basis of M2,2- O sis not a basis of…

A: The given set,S=4003, 1402, 2230, 0120

Q: Determine whether S is a basis for P3.S = {−1 + t3, 2t2, 3 + t, 5 + 2t + 2t2 + t3}

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Q: Let S = {(a, b, c, d) | a, b, c, d ∈ R, a = c, d = a + b}. Find a basisfor S.

A: Since a = c and d = a + b this means c and d are linearly dependent. Hence, out of four vectors,…

Q: Let A = {(0, –1,6); (–1,0,2); (2,1,0)} . Then A is a basis for

A: Introduction: A set of vectors in V is the basis of V if the set is linearly independent in V.

Q: Check whether the set V= {(2, 3), (3, 4)} is basis of R2 or  not?

A: this a spanning set and linearly independent so the vectors forms a basis of R^2

Q: Explain why S is not a basis for M 2 O sis inearly dependent. Os does not span M O si inearty…

A:

Q: Explain whether S = {(1,0,0), (0,2,0), (–4,0,1), (0,5,0)} is a basis for R³ or not.

A:

Q: I Let 6 A = --2 -2 -4 -2 -2 -4 Find a basis for the null space of A. {

A: Let us consider matrix A of order n x m. The null space of matrix A is defined as: Null(A)=x∈Rm|Ax=0…

Q: Apply Gram-Schmidt method to change {{:)} into an orthonor- mal basis {u¡, u2} of R² .

A: We have to find the orthonormal basis for the given set.

Q: Is it {C1,-1, 0,2), (3,-1,2,1)( 18,0,1)3 R Basis ?

A: The objective is to solve the above question.

Q: 12. The et 5 - {; 96 1A}- is: a. a basis of M22- b. not a basis of M2,2.

A: The standard basis of M2,2 is: e1=1000 ,   e2=0100 ,     e3=0010 ,    e4=0001

Q: How is the basis {lk} picked?

A:

Q: 17. Find a basis for W-, where 2 W = span 3 7 4 8

A: We have W=span1234, 5678 The basis for W⊥ is the null space of the matrix formed by the rows made of…

Q: Determine whether (V₁, V2, V3) is a basis for R³. V₁ = No O Yes V₂ = 8 s 3 V3 -2 [-7]

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Q: B/Show if the set below is a basis for M2x2 or not -2 3 3 4 -3

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Q: Find the value of Blank-1 Basis Cij 5.58X1 4.5X2 5.36X3 S1 52 аз RHS X3 5.36 -0.125 -0.125 -0.75…

A: The objective is to fill the value of Blank -1 The table is given as,

Q: Tawing questions

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Q: Explain why S is not a basis for M2,2.

A: The set is S=1000,0110,1001,8-4-43   Known fact: A set of vectors S=v1,v2,…vn is a linearly…

Q: Consider the following. Complete the following statements. The elements of set B ---Select--- |…

A: Given,          V=M11,             B=1001, 1011,    1-1-1  1

Q: Determine whether the following is a basis. 1.S %3D (4 - х, х3, 6х?, х3 + 3х, 4х — 1} | [2 0* [1 0.…

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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.