Let M ={ 1- 1-6 E 3 Then M not basis for M2.2 because the number of elements in M is not equal to the dimension of M2.2

Q: Which of the following is the standard basis of M22? 0. 0. 0. Lo o][1 o]* o 0. 0 1] 0 0 1.

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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: Given that the set (1, 1+x+x,p(x)} is a basis for AX = P,, which of the following is a possible…

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Q: 3 1 1 S = span -2 3 -4

A: S=span 10-11,2003,31-20,01-1-4

Q: Let S then S is a basis for R C

A: S = ( 12, -1c ) So set S to be a basis of a given vector space the vectors should be linearly…

Q: 2.) Determine whether S = {G.1).(1.0).(2,12,6)} is a basis for R. If it is write u = (6,3,6) as a…

A: Determine whether S=23, 52, 1, 1, 32, 0, 2, 12, 6 is a basis for ℝ3. A set of linearly independent…

Q: Let S = {2x, 1 - x, x² + x-1, x + 1,X P2 S is a basis for the above P1 S is a basis for the above P3

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Q: If R has the basis {e,, e,, e}, therefore the dimension of R is Select one: O A 3 O B. greater than…

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Q: Let M = {(, Then M is a basis for M3,2 O None of the mentioned O the above M2,3 the above

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Q: Every basis for R4 contains

A: Every basis of ℝ4 contains ______________

Q: 1- The vectors x, = (2,1, –4), x2 = (-3,4,1) and x3 = (2, –1,3) %3D %3D in R3, are A: represent a…

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

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Q: The following solution of LPP Problem is given: Basis 6 10 9 B X1 x2 X3 X4 x5 X6 minß,(8) X4 120 15…

A: Lpp: simplex method

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.…

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

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Q: Let M = { : 9-6 ¿ 6:9C: 9C : } Then M is a basis for None of the mentioned M2,3 O the above M3,2 O…

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Q: O Is the sed 5-[2],[2 1]" basis for R".

A: A basis is linearly independent and spans the space   We are allow to solve first question only. If…

Q: Show that the following set is not a basis of R4: 1 3 2 2 3 15 1 -3 2 -17 2 -3 13

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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: Let M = {C : )-C : )-C : 26:96: Then M is a basis for M23 the above None of the mentioned M3,2

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Q: Let S = (2x, 1 - x, x2 +x 1,x+ 1}. Then PA P1 O sis a basis for the nbove Sis a basis for the above…

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Q: 1) Which of the following sets of vectors is a basis for R: b) LD d) {}

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Q: Let M = {[; 1-C %3D Then M is a basis for

A: Final Ans: None of the Above

Q: Find a basis for the null space of the matrix. A = C C [10-40-4] 01 20 2 00 01 1 100 00 0 42100 0 0…

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Q: Find a basis for N(A) and give the nullity and the rank of A. -1 2 0 A 2 -5 1

A: Suppose A is any mxn matrix then RankA+NullityA=n

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: 2. Determine whether the set S = {(2, 0, 1), (2, -1, 1), (4, 2, 0), (-6, 2, 3)} a. Spans R3 b. Is…

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Q: Let O 0 10 -1 A = |0 0 0 1 3 1 4 0 0 A basis for Null(A) is given by:

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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: Prove that if S= {v1, V2,..., Vn} is a basis for V and c is a nonzero constant, then S {cV1; cV2,…

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Q: Determine whether S is a basis for M2.2. 2 0 2 4 0 1 5. 0 2 4 0 O S is a basis of M2,2. O S is not a…

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

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Q: Determine whether S is a basis for M2.2. -{::}| 2 0 2 0 0 1 0 1 S = 0 5 5 1 3 2 2 0 O sis a basis of…

A: Since given set is finite if it is linearly independent then S is basis. Show that S is linearly…

Q: c) Find a subset of S that is a basis for W.

A: A linearly independent set of vectors is a basis of a subspace W if it spans W. Now since S spans W,…

Q: Let S = {2x, 1 -x,x² + x - 1,x + 1,x – 2}. Then None of these P2 S is a basis for the above P.

A: S is said to be basis of R3 if S is linearly independent L(S) = R3

Q: Let B= { }],}} 3 -3 2 2 -1 be basis for IR Find [v]a where 15 6- 3.

A: Find the determinant of vectors of B to check linear independent. We have to Express v as a linear…

Q: 2) Determine whether S = {(0,3,-2), (4,0,3)(-8,15, -16)} is a basis for R3.

A: Given that, S=(0,3,-2),(4,0,3),(-8,15,-16)

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

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

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Q: Determine whether S is a basis for P3. S = {1 - 212 + 3, -3 + 2, 2t + t, 6t} O is a basis of P3. O…

A: The given set is: S= 1-2t2+t3,  -3+t2,  2t+t3,  6t

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

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Q: The following is a simplex tableau: Basis Св 5.85 9.43X1 4.5X2 5.85X3 S1 S2 RHS аз X3 S2 X1 -1.25…

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Q: 2. Let S ={2 , 1 in M31. a. Determine whether S spans M31. b. Determine whether S is linearly…

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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: 1 2 1 1 Let U1 = 1 U2 = 1 V3 V4 1 1 t For what of value of t is the set{v1, v2, V3, v4 NOT a basis…

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Q: Consider the limear thans femartin IC) - Ax de fiva by te matrix Ac 20 23 1 34 2 2 2. 1 20 D Find a…

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Q: Given the set S = {M1, M2, M3, M4}, where 3 1 2 M1 = M2 2 4 1 -3 0 -2 1 1 M3 M4 4 1 2 -1 (a) Show…

A: We will find out the required solution.

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…