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

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: Explain why S is not a basis for R2.S = {(2, 3), (6, 9)}

A: We know the basis of R2 = {(1,0),(0,1)} So it has 2 elements So, another basis of R2 also must have…

Q: 2. Let L1 bg 3D (-1,2, 1,3, 3), сі %3D (3, —4, 0, — 4, 3), сэ %3D Find a basis of Lin L2 and L1+ L2.…

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Q: If A = {v1, v2, ..., vn} be a basis for FV and n ≥ 2 then, is B = {v1+v2, , v2+v3, ..., vn+v1} also…

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Q: Let 4= [ -1 1 2 4 -2 2 Find an orthonormal basis of the row space of A.

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Q: How are n, rank A, and nullity A related to each other how can one find a basis for Col A, Nul A,…

A: Write the relationship between n, rank A and nullity A. Also write a procedure to find a basis for…

Q: Let 1 1 -4 A = -3 9 -6 -2 8 -7 Find an orthonormal basis of the column space of A. 4 -18/5 -6 36/5

A: Consider the matrix A=[11-4-39-6-28-7]We find the basis for the…

Q: (16v2,2v2) is any B = {(, -),,)} be an orthonormal basis for R. If Let vector in R, determine the…

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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: The vectors 7 -6° Ú2 = 2 -3 form a basis for R³ if and only if k + Submit answer

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Q: Iř bị, b2 form an orthonormal basis for C and x is any vector in C?, then O x[4 – 2 |x - b1|² |x -…

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Q: Determine if 3 W = { |-4 2 |} 3 -5 %3D 3 4 -2 is a basis for R. Justify your answer.

A: Given set, W=1-43,03-1,3-54,02-2. To check W is a basis for R3. To check W is a basis, we have to…

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

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Q: Find the basis for the Null space of the matrix 1 4 5 2 1 3 0 1 3 2 2 A = 2

A: A=14522130-1322 →R3→R3+R1R2→R2-2R1…

Q: 6. Determine the basis for the null space of -2x + 2y + 2z] a) 3x + 5y + z 2y + z х — 2у — z b) -x +…

A: Introduction: Null Space, like Row and Column Space, is a simple area in a matrix, including all…

Q: Extend {u1=(1, 1, 1, 1); u2=(2, 2, 3, 4)} to a basis of R4.

A: Extend {u1=(1, 1, 1, 1); u2=(2, 2, 3, 4)} to a basis of R4.

Q: 4 4 A = -2 3 3 3 2 1 1 -2 Basis

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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: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: Assume that: U1= -1 -1 u2= 1 And W=span {U1, U2}. -Find a basis to W-.

A: Here   u1 , u2 are two vector. W= span {u1, u2 } So, {u1 , u2 } is a basis . Now we found a basis ,…

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

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Q: Is R={(2,0,1), (2,-1,1), (4,2,0)} a basis for R²? Yes or No? Justify or give/find a counterexample.…

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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

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Q: Find a basis for the column space of -4 41 -2 -4 4 -3 0 -3 2 Basis =

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Q: Let A = {(1,0,-2); (2,1,0); (0,1, –5)} . Then A is a basis for %3D

A: set A contains 3 vectors  So, A is a basis for R3.

Q: If b1, b2 , b3 is a basis of IR and A, B are 4 × 3 matrices satisfying Ab; = Bb; for i = 1, 2, 3…

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Q: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: 2.) Determine whether S = is a basis for R³. If it is write u = (6,3,6) as a linear combination of…

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

A: We have given a set of the matrices;

Q: 1 2 A basis of the null space of 2 4 -2 -3 -6 3 (A) {(-2,1,0), (1,0, 1)} (В) {(-2, 1, 1)} (С)…

A: A detailed solution is given below.

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

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

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

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Q: Let 1 1 -5 A = -2 2 -2 2 -3 Find an orthonormal basis of the column space of A. {

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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: 4 2 If a basis for R3 is B = and if a vector in the standard basis is i = |-4|, find its 5…

A: We know, The set B of vectors in a vector space V is called a basis if every element of V can be…

Q: 5

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Q: 4. Find a basis of the nullspace of 2 -6 5 -8 A = 1 -3 1 -1 3 -9 4 -5

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

A: It is known that,

Q: .. Find A basis for the nullspace and column space of 1 2 1 1 2 2 2 4 3 2 1 1 2 A = 3 3 1 -1 -1 |

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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: 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: |Let -2 1 -3 A 7 -1 Find an orthonormal basis of the row space of A.

A: Use Gram -Schmidt Orthogonalization process to find the orthonormal basis of the row space of A.

Q: a)show that { d,b',7} it's a basis

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Q: Lemma 2.8 B is a basis of Tiff VOETBCB: 0=U Bo

A: To show: B be a basis of τ iff for all O belongs to τ ∃ BO⊂B: O=∪BO

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.